To start off I will give descriptions of both characters.
EDWIN JARVIS:
Jarvis served in the British RAF during World War II and was its champion boxer three years running. He later moved to America where he became manservant to the Starks (Howard and Maria) and watched over their mansion even after their deaths.
Anthony "Tony" Stark (the son of Howard and Maria) called the first meeting of the Avengers as Iron Man and donated the house as headquarters, so that it became Avengers Mansion. Jarvis grew accustomed to the guests and served the Avengers for many years thereafter, acting as a father figure to some of the newcomers. He was the only one to stay with the Avengers for their entire existence, a distinction not even Captain America can claim. As a result, Captain America has stated that Jarvis should be regarded as just as much of an Avenger as he is.
Jarvis spent some time as the primary babysitter for Franklin Richards, the super-powered son of Mister Fantastic and the Invisible Woman when they were residing at the mansion. He also served as the sponsor to future Avengers member Silverclaw while she was growing up, and she has come to regard him as an uncle.
Being manservant to the Avengers meant that Jarvis has had to deal with their enemies himself on several occasions. In Avengers #59 and #60 (December 1969, January 1970) he was assaulted by intruders into the mansion and bound and gagged. He has also been involved personally in many adventures, including leading the evacuation of a stalled subway train during a city-wide disaster and battling a demonically possessed car. During this time he dated a woman he rescued named Glory. Jarvis defended the floating Hydrobase against a horde of robots built by Doctor Doom during the Acts of Vengeance crisis. He was present when one of the many incarnations of the Masters of Evil attacked the mansion. He was brutally beaten by Mr Hyde while Captain America was forced to watch. It took some time for Jarvis to recover from his injuries. He even wore an eyepatch for some time. Jarvis personally confronted Loki, risking great danger, after realizing the villain had tricked his way inside the mansion in Avengers #400.
In his duties as the Avengers' manservant, he was entrusted with items of great power, including the Casket of Ancient Winters.
When the New Avengers were formed, Jarvis was called back after taking a holiday "for the first time in years", having been informed that his 'special' services were once again needed. Jarvis often confronts Wolverine over the man's poor kitchen etiquette, a battle only new member Spider-Man's Aunt May was able to win. Jarvis struck up a relationship with May, who had moved into Stark Tower with Peter and Mary Jane after her house burnt down. When Spider-Man switched sides during the Civil War, however, Aunt May and Mary Jane fled Stark Tower to live in hiding.
In a New Avengers "Civil War" story, Jarvis was shot by an employee of Tony Stark, who was opposed to Stark using technology he invented to enforce the Superhuman Registration Act. However, it appears Jarvis recovers from this wound, as in "Civil War: The Initiative", he is shown to be working again. He also humorously mentions that if Tony Stark allowed "that Tigra %^#$" in the new incarnation of the Avengers, Tony would need to find someone else to do the laundry. Tigra had worked for Tony Stark's side throughout the entirety of the Civil War incident.
In the 2008 storyline "One More Day", Jarvis is given over $2,000,000 by Stark to pay for the hospital bills Aunt May's hospital bills following an assassination attempt in the aftermath of Spider-Man's decision to publicly reveal his true identity. Jarvis visibly breaks down upon seeing her in the hospital bed, confessing his deep love to the Parkers. As a consequence of the "One More Day" storyline, however, the Spider-Man comics have undergone a major continuity overhaul, including Jarvis' relationship with the Parkers. An issue of New Avengers is advertised as addressing Spider-Man's "new" history with the team, which would include this time period.
Later that year, in the "Secret Invasion" storyline, it is revealed that Jarvis has been replaced by a Skrull agent (though the exact time is unclear, it was revealed in a summary of "Secret Invasion",when describing the Jarvis Skrull, that it was before Jarvis started his relationship with May).Using a computer virus, he disables a number of Stark Enterprises facilities, as well as Stark's armor. This agent also obtained access to Tony Stark's records on Robert Reynolds (The Sentry) in order to discover his weaknesses, as the Skrulls were unable to duplicate his powers because its limits were unknown even to Stark.He later approaches Maria Hill on the destroyed S.H.I.E.L.D. Helicarrier in the middle of the ocean and tells her to surrender along with her crew. She uses a Life Model Decoy in that spot as the real one escaped and detonated the S.H.I.E.L.D. Helicarrier. During the fight between Veranke and Criti Noll's forces against the heroes and villains, The Skrull-Jarvis (who somehow survived the S.H.I.E.L.D. Helicarrier explosion) watches from Avengers Tower as the energy washes over hero, villain and Skrull alike. While holding Jessica Jones and Luke Cage's child, he comments that it doesn't matter if the Skrulls win or lose, so long as "God's" will is done.
After the final battle, the real Jarvis is discovered alive, prompting Jessica Jones to discover that her baby had been taken by the Skrull impostor. Jarvis is later shown in a support group meeting with the others that had been replaced by Skrulls.The Skrull Jarvis was eventually found in a hideout and was shot by Bullseye after returning the baby to Luke Cage.
During the "Earth's Mightiest" story arc, the real Jarvis, having refused to serve under Norman Osborn's new group of Avengers is sought out by Hercules and Amadeus Cho to be a part of the new Mighty Avengers team, Amadeus having determined that Jarvis is the one constant of the Avengers.
ALFRED PENNYWORTH:
When Alfred first appeared, he was overweight and clean-shaven; however, when the 1943 Batman serial was released, William Austin, the actor who played Alfred, was trim and sported a thin moustache. DC editors wanted the comic Alfred to resemble his cinematic counterpart, so in Detective Comics #83 (January 1944), Alfred vacationed at a health resort, where he slimmed down and grew a mustache. This look has remained with the character ever since, even surviving his "death" and resurrection.
Alfred was originally conceived as a comedic foil for Batman and Robin. In most early tales, he made bungling attempts to be a detective on a par with the young masters. He was given a four-page feature of his own,and the feature lasted thirteen issues, skipping Batman #35, with the last story in Batman #36. The stories followed a simple formula with Alfred somehow managing to solve a crime and catch the culprits entirely by accident. After that, the comedic aspects of the character were downplayed.
The Pre-Crisis comics (the comics that were published by DC Comics between 1938 and 1986) established Alfred as a retired actor and intelligence agent who followed the deathbed wish of his dying father, Jarvis, to carry on the tradition of serving the Wayne family. To that end, Alfred introduced himself to Bruce Wayne and Dick Grayson at Wayne Manor and insisted on becoming their butler. Although the pair did not want one, especially since they did not want to jeopardize their secret identities with a servant in the house, they did not have the heart to reject Alfred.
Alfred in his first appearance as an overweight, bumbling detective.Initially, Alfred discovered their identities by accident; while fighting a burglar in Batman #16 (Alfred's first appearance), he accidentally hit a switch and opened a sliding-panel leading to the Batcave. He is helpful to the Duo, following them to a theatre where they are captured, bound and gagged by a criminal gang, and rescues them after Batman attracts his attention by knocking a rope down before the crooks return. This was revised in Batman #110 (September 1957); during his first night at Wayne Manor, Alfred awoke to moaning (Batman had been injured out in a field) and followed the sound to the secret passage to the staircase leading to the Batcave and met his would-be employers in their superhero identities. As it turned out, the wounds were actually insignificant, but Alfred's care convinced the residents that their butler could be trusted. Since then, Alfred included the support staff duties of the Dynamic Duo on top of his regular tasks.
Ironically, Alfred's loyalty would lead him to become a member of Batman's rogue's gallery. While pushing Batman and Robin out of the way of a falling boulder, Alfred was seemingly killed in Detective #328 (June 1964). It was revealed in Detective #356 (October 1966) that he had been revived by a scientist named Brandon Crawford. His attempt at regeneration resulted in a dramatic change: Alfred awoke from his apparent death with pasty white skin with circular markings, superhuman powers, including telekinesis, and a desire to destroy Batman and Robin. Calling himself The Outsider, he indirectly battled the Dynamic Duo on a number of occasions, using others as his puppets – the Grasshopper Gang in Detective #334, Zatanna in Detective #336, and even the Batmobile itself in Detective #340 – and generally only appeared as a mocking voice over the radio. He did not physically appear in the comics until Detective #356, when he is bathed again in the rays of the regeneration machine during a struggle with Batman, and returns to normal, with no memory of his time as a supervillain. His time as the Outsider is collected in Showcase Presents: Batman Volumes 1 and 2.
Alfred was later reunited with his long-lost daughter, Julia Remarque, though this element was not included in Post-Crisis comics. Her mother was the DC war heroine Mademoiselle Marie, whom Alfred had met while working as an intelligence agent in occupied France during World War II.
In the Post-Crisis comics' continuity, Alfred has been the Wayne family butler all of Bruce's life, and had helped his master establish his superhero career from the beginning. In addition he was Bruce's legal guardian following the deaths of his parents. Alfred's history has been modified several times over the years, creating assorted versions. In one such version Alfred was hired away from the British Royal Family by Bruce's parents, and he virtually raised Bruce after they were murdered.
Meanwhile another version of Alfred's Post-Crisis life was slightly more closely linked to his pre-Crisis counterpart. In this version Alfred was an actor on the English stage, who agreed to become the Waynes' butler, only so as to honor the dying wish of his father. At the time he begins working for the Waynes, Bruce is but a young child. After several months, Alfred voices the desire to quit and return home to continue his life as an actor. However, these plans are momentarily forgotten when young Bruce returns home, after getting into a fight with a school bully. Alfred teaches Bruce to handle the bully strategically, rather than using brute force. Following Alfred's advice, Bruce manages to take care of his bully problem. Upon returning home, Bruce requests that Alfred stays, and Alfred agrees without a second thought. After the Waynes' murders, Alfred raises Bruce.
Alfred would later aid Bruce in raising Dick Grayson, Jason Todd, and Tim Drake, all of whom would be adopted by Bruce Wayne and become his partner Robin. He also had close friendships with other members of the Bat-Clan including Barbara Gordon and Cassandra Cain. Alfred often acts as a father-figure to Bruce, and a grandfather to Dick, Jason, and Tim. He is also highly respected by those heroes who are aware of his existence, including Superman, Wonder Woman, Green Lantern, and the original Teen Titans.
Alfred has also been romantically linked to Dr. Leslie Thompkins, though his relationship with her never came to anything, particularly after she apparently allowed Stephanie Brown to die from neglect. He also developed feelings for Tim Drake's stepmother, but again, nothing came of it.
During the events of Knightquest, Alfred accompanies Wayne to England, and becomes enraged when Wayne insists on endangering his own health while paraplegic. This was the culmination of several weeks of Wayne's self-destructive behavior, and when Wayne returns to Gotham City, Alfred remains in England, tendering his resignation. He spends some time vacationing in Antarctica and The Bahamas before returning to England. Dick Grayson tracks him down several months later and convinces him to return to Wayne Manor. In that story, it was revealed he had walked out of his own wedding years earlier.
His resourcefulness came to the fore in the No Man's Land storyline, especially in Legends of the Dark Knight #118. Batman is missing for weeks, leaving Alfred alone to watch his city for him. He uses his skills as an actor, storyteller, medic, and spy to survive and collect information on the recently destroyed society. Alfred even uses hand-to-hand combat in a rare one-panel fight sequence between him and a pair of slavers that ends with his rescue by Batman.
In Batman #677, agents of Batman's mysterious enemy the Black Glove attack and beat Alfred in front of Bruce and Jezebel Jet, severely injuring him. In the same issue, a reporter from The Gotham Gazette suggests to Commissioner Gordon that Alfred may be Bruce's biological father, and that this may be a reason for the murder of Martha Wayne. Alfred later denies the entire story, agreeing with Bruce that it was a fabrication. In Batman and the Outsiders Special, Alfred is seen apologizing at the graves of Thomas and Martha Wayne at the loss of Bruce, commenting that he grieves as a parent, regarding Bruce as his son. Later, a secret panel in Alfred's room opens, the result of a failsafe planted by Bruce in the event of his death. Bruce leaves his one final task, and also gives him an emotional goodbye, telling Alfred he considered him as a father. Alfred is left emotionally shattered, commenting more than once that, even if his biological fatherhood is a fabrication, in a deeper sense he actually was Bruce Wayne's father, having watched over him for years and feeling to have failed him in the last moments.
After the event of Final Crisis, Alfred finds himself with the task of raising Bruce's biological son Damian with Dick. Batman: Battle for the Cowl sees Alfred allowing Damian Wayne to take on his first mission as Robin, giving Damian a Robin tunic and calling on Squire to assist the new Boy Wonder in finding Tim Drake, who went missing hunting down Jason Todd.
In the absence of Batman, the Outsiders will be led by a new Owlman. A Trick or Treat tease from the Oct. 2008 of DC Nation hints that it will be Alfred Pennyworth behind the mask. In Origins & Omens: Outsiders #15, however, Alfred takes the role of leader of the Outsiders unmasked (directing them remotely). Owlman is revealed to be Roy Raymond Jr., a former television mystery show host, who was hand-selected by Batman prior to his death.
Alfred is quite a brilliant man. He primarily keeps up day-to-day operations of Batman’s home of Wayne Manor and maintains much of the equipment of the Batcave beneath it. A former actor, he can use his acting and disguise skills to help Batman in the field when necessary, and is even capable of impersonating Bruce Wayne on the telephone convincingly. He has also provided first aid up to and including suturing wounds and removing bullets, as well as occasional tactical support. With time, he has increased his surgical skills, and he's now able to perform arthroscopy and other advanced medical procedures, thus limiting, if not eliminating, the need for hospital medical treatment even in the face of grievous injuries (Although professional medical treatment was still required when Bruce's back was broken by Bane (Batman: Knightfall) and when he sustained a skull fracture due to the machinations of Hush (Batman: Hush), Alfred noting that his own skills were inadequate for the current tasks).
While not as skilled at hand-to-hand combat as Bruce Wayne, Alfred is still nearly as resourceful. During a time at which he was kidnapped, he readily escapes and overcomes his captors without disturbing the cut of his suit. It was later mentioned that he had been kidnapped unsuccessfully 27 times (it should be noted, however, that these events take place in the Gotham Adventures comics, based on the animated adventures of Batman, and not within the standard DCU continuity).During Batman: The Resurrection of Ra's al Ghul, Ubu, Ra's massively muscled bodyguard and henchman, attempts to use Alfred as a hostage, only to be disabled by a well timed sucker punch from Alfred.
Presumably due to his lack of superpowers, the advanced combat training Bruce's other associates have, and Alfred's age, Alfred is the only member of the "Batman Family" that Bruce does not mind using a firearm, in his case favoring a shotgun when dealing with direct attacks on his person.
Current issues of the various Batman comics seem to indicate that Alfred is a pioneer in and has also mastered several fields of rose breeding (even creating his own, the "Pennyworth Blue"), computer programming, computer engineering, electrical engineering, chemical engineering, mechanical engineering, nanotechnology, and biotechnology as he singlehandedly builds, programs, and maintains much of Batman's next-generational technology such as the Batcomputer.