Rules: The swap would be permanent. You can either switch the characters as they are, or make it as if they were always part of their new universe (Thor dicking around on New Genesis as opposed to Aquaman being Namor's...brother or bastard son or something.). To keep things fair, you can only swap equivalent characters. Whether that means personalities or powers or their scale is up to you. Spider-Man for Dick Grayson: Good. Stilt-Man for Darkseid: Not good. You can swap as many of their supporting cast as you want, or none at all. How quick would Lois Lane figure out who Spider-Man was if he worked at the Daily Planet? How would Batman function without Alfred?
To make an example, Superman swapped with Captain America. You can be as detailed or as broad as you like.
Steve Rogers served in World War 2 as Captain America and fought alongside the Justice Society with his kid sidekick Bucky. They were both presumed dead when stopping an attempt by the Ultra Humanite to drop an Atomic Bomb on the United States. Cap gets frozen, Bucky is claimed and resurrected by the League of Assassins. When Cap is thawed out sometime in the late 80s, he's amazed that Jay and Alan are still fighting the good fight, but is saddened that the JSA were forced to disband, knowing that if he were alive at the time, he would have stepped up and stopped the madness. Other than that, all Steve can do is try to catch up with the times and get back into action. In a world without Superman, Batman never learns to trust other heroes and never joins the Justice League, so Captain America is the team's tactician and moral compass. Cap does not care much for CADMUS, though he respects Amanda Waller's moxie. When Batman loses Jason Todd, even though they've never treated each other as friends, Steve is the first one there for Bruce to talk to. In turn, Bruce is there for him when Bucky comes back from the dead. Also in this Superman-less world, Lex Luthor's enemy is Metropolis's favorite son, Captain Marvel (A huge Captain America fan). But that's neither here nor there. Oh, and Cap and Diana probably have an on-and-off thing. When Luthor runs for president, Steve also decides to run (with Jefferson Pierce as his running mate), and nearly wins, losing by a single vote.
Kal-El was sent to Earth when his planet was being destroyed by Galactus, who came to Krypton after their enemies, the Skrulls, blacked out their planet to trick Galactus. He landed on Earth in the Kansas wheat fields, where SHIELD knew about his arrival almost immediately, but Nick Fury told them to just observe his growth. Kal-El was adopted by John and Martha Kent, who gave him the name Clark. Clark's powers started to develop in his early teens, but his parents never told him about his being an alien because they were worried about how he'd cope with it. So, Clark's first assumption is that he's a mutant, and he goes to the Xavier Institute. He's there just long enough to form bonds with the X-Men, buddying up with Bobby and Hank, flirting with Jean, butting heads with Scott, but then Xavier tells Clark that, whatever it is, however powerful that something might be, he is not a mutant, and has to leave. Clark continues his cross-country not-yet-Superman adventures, including meeting the Fantastic Four and temporarily working with them while Reed Richards tries to analyze his blood. His results, as well, are inconclusive. Only that Clark is definitely not human. Whatever he is, Clark finally becomes Superman in New Mexico, where he intervenes against a rampaging Hulk before the newly-formed Avengers can intervene. Put on the spot, Clark calls himself Superman, and is offered to join Ant-Man, Thor, Iron Man, and Wasp on The Avengers. Desperate for any sort of people like himself, Superman takes them up on that offer. Even the perpetually-negative populous of the Marvel universe can't hate Superman, whose very existence improves Metahuman/Human relations, and he often speaks out on Mutant Rights issues. He's friends with Spider-Man and Thor (to name a few), thinks Nick Fury's kind of an asshole, and doesn't much care for Namor. Superman's primary enemy is Dr. Doom (if you can think of a better Luthor stand in or a better villain in general, I'm all ears), and he finds out the truth of his origin during the Kree-Skrull war, earning a special hatred for Skrulls and Galactus. Clark has a couple short-term relationships, including with Janet Van Dyne, Storm, and of course, She-Hulk ('cause the Marvel universe always seemed a bit more swinger-y than DC, to me). But, eventually he settles down with "The most captivating woman I've ever met", Carol Danvers, aka Captain Marvel.
Rules: The swap would be permanent. You can either switch the characters as they are, or make it as if they were always part of their new universe (Thor dicking around on New Genesis as opposed to Aquaman being Namor's...brother or bastard son or something.). To keep things fair, you can only swap equivalent characters. Whether that means personalities or powers or their scale is up to you. Spider-Man for Dick Grayson: Good. Stilt-Man for Darkseid: Not good. You can swap as many of their supporting cast as you want, or none at all. How quick would Lois Lane figure out who Spider-Man was if he worked at the Daily Planet? How would Batman function without Alfred?
To make an example, Superman swapped with Captain America. You can be as detailed or as broad as you like.
Steve Rogers served in World War 2 as Captain America and fought alongside the Justice Society with his kid sidekick Bucky. They were both presumed dead when stopping an attempt by the Ultra Humanite to drop an Atomic Bomb on the United States. Cap gets frozen, Bucky is claimed and resurrected by the League of Assassins. When Cap is thawed out sometime in the late 80s, he's amazed that Jay and Alan are still fighting the good fight, but is saddened that the JSA were forced to disband, knowing that if he were alive at the time, he would have stepped up and stopped the madness. Other than that, all Steve can do is try to catch up with the times and get back into action. In a world without Superman, Batman never learns to trust other heroes and never joins the Justice League, so Captain America is the team's tactician and moral compass. Cap does not care much for CADMUS, though he respects Amanda Waller's moxie. When Batman loses Jason Todd, even though they've never treated each other as friends, Steve is the first one there for Bruce to talk to. In turn, Bruce is there for him when Bucky comes back from the dead. Also in this Superman-less world, Lex Luthor's enemy is Metropolis's favorite son, Captain Marvel (A huge Captain America fan). But that's neither here nor there. Oh, and Cap and Diana probably have an on-and-off thing. When Luthor runs for president, Steve also decides to run (with Jefferson Pierce as his running mate), and nearly wins, losing by a single vote.
Kal-El was sent to Earth when his planet was being destroyed by Galactus, who came to Krypton after their enemies, the Skrulls, blacked out their planet to trick Galactus. He landed on Earth in the Kansas wheat fields, where SHIELD knew about his arrival almost immediately, but Nick Fury told them to just observe his growth. Kal-El was adopted by John and Martha Kent, who gave him the name Clark. Clark's powers started to develop in his early teens, but his parents never told him about his being an alien because they were worried about how he'd cope with it. So, Clark's first assumption is that he's a mutant, and he goes to the Xavier Institute. He's there just long enough to form bonds with the X-Men, buddying up with Bobby and Hank, flirting with Jean, butting heads with Scott, but then Xavier tells Clark that, whatever it is, however powerful that something might be, he is not a mutant, and has to leave. Clark continues his cross-country not-yet-Superman adventures, including meeting the Fantastic Four and temporarily working with them while Reed Richards tries to analyze his blood. His results, as well, are inconclusive. Only that Clark is definitely not human. Whatever he is, Clark finally becomes Superman in New Mexico, where he intervenes against a rampaging Hulk before the newly-formed Avengers can intervene. Put on the spot, Clark calls himself Superman, and is offered to join Ant-Man, Thor, Iron Man, and Wasp on The Avengers. Desperate for any sort of people like himself, Superman takes them up on that offer. Even the perpetually-negative populous of the Marvel universe can't hate Superman, whose very existence improves Metahuman/Human relations, and he often speaks out on Mutant Rights issues. He's friends with Spider-Man and Thor (to name a few), thinks Nick Fury's kind of an asshole, and doesn't much care for Namor. Superman's primary enemy is Dr. Doom (if you can think of a better Luthor stand in or a better villain in general, I'm all ears), and he finds out the truth of his origin during the Kree-Skrull war, earning a special hatred for Skrulls and Galactus. Clark has a couple short-term relationships, including with Janet Van Dyne, Storm, and of course, She-Hulk ('cause the Marvel universe always seemed a bit more swinger-y than DC, to me). But, eventually he settles down with "The most captivating woman I've ever met", Carol Danvers, aka Captain Marvel.
My various fanfics.