Heroes and villains are frequently victims of circumstances. As Joker once told Batman in The Killing Joke, "All it takes is one bad day to reduce the sanest man alive to lunacy." A hero in one situation is a villain in another, depending on context and, to be frank, point of view. If you remove a hero from the circumstances that make him or her a hero, it's quite easy to become a villain.
Take the heroes of the DC Universe. In some cases, moving them to another universe might be all it takes to turn them into the bad guys.
10 Huntress
To be frank, Huntress is just barely a hero in her own universe. An unwilling part of the extended Bat Family, Huntress has always toed the line between hero and villain, with a greater willingness to cross it than Batman. Her penchant for violence combined with her underlying rage make it hard for other heroes to trust her but she stays on the side of the angels thanks to the friends she has.
Once in the Marvel Universe, it would be easy for her to give in and begin killing, something that wouldn't go over well with the heroes there. Well, except Punisher. They might become besties.
9 Batman
The Caped Crusader would present quite a conundrum for the heroes of the Marvel Universe. On one hand, Batman is one of the staunchest heroes DC has to offer, saving Gotham, the world and the universe on multiple occasions. On the other hand, he can also be a paranoid lunatic who spends a surprising amount of time figuring out how to take down his allies.
Batman sees the world in stark contrasts of black and white, and the Marvel Universe is filled with shades of grey. Left alone in the new universe, Batman would find himself the villain quite quickly. That being said, he still wouldn't slip into Batman Who Laughs territory.
8 Hawkman
The policeman from another planet who has been reincarnated over and over again has been part of DC for almost as long as there has been a DC. Hawkman can fly, is super strong and is an expert with an variety of weapons. When he arrived on Earth, he became one of its most respected heroes.
One would hope that the same would be true if he made his way to the Marvel Universe. In reality, Hawkman would find himself almost immediately at odds with the likes of Thor and Captain America due to his authoritarian outlook on being hero combined with his barbaric methods.
7 Martian Manhunter
The last Green Martian has an impressive assortment of powers that put him on par with DC's best, including Superman. Unfortunately, he also has one of the most mundane weaknesses and can be taken out by someone surrounding him with lit torches. Martian Manhunter often struggles to find acceptance in his own universe, constantly searching for a place he feels comfortable.
He often plays the part of an outcast. In the Marvel Universe where mutants are routinely persecuted, the Manhunter's experience would be even worse. He would find himself allied with the likes of Magneto in the fight for non-human rights.
6 Doctor Fate
Regardless of who wears the Helm of Nabu, Doctor Fate would find himself at odds with the heroes of Marvel. Magic is often a difficult thing for most heroes to handle but Marvel has people like Doctor Strange to help them navigate those waters. Unlike Strange, Fate is far more cold, calculating and removed from humanity, in no small part due to the influence of Nabu.
He is a defender of Order, which usually aligns with what's right. But the Marvel Universe is much more chaotic than DC, and Fate would certainly runs afoul of someone like the Scarlet Witch who manipulates chaos magic.
5 Deadman
An acrobat in life, Deadman was murdered by the League of Assassins and became a ghost charged with possessing the living to save them from damnation. That's a lot of pressure. As a ghost, Deadman exists on the periphery of everything happening in the DC Universe, only ever really able to communicate with the living when he's possessing someone.
It would be harder for him to fit in the Marvel Universe which is filled with mystical forces that can be almost impossible to trust. Deadman would find himself even more excluded there than in DC and eventually cast in the role of villain.
4 Raven
The demonic daughter of Trigon, Raven fights for good alongside her fellow Teen Titans while trying to suppress her own evil instincts. Every fiber of her being screams at her to do horrible, evil things but her friends help her not to. Once in the Marvel Universe, separated from the other Titans, Raven would end up giving in and using her powers to their fullest, worst potential.
A hero in the DC Universe, she could quite easily become one of the most devastating villains in the Marvel Universe. That, or she'd just start hanging out with the Runaways and everything would be fine.
3 Starfire
Another longstanding member of the Titans, Starfire is a warrior princess from the planet Tamaran. On Earth, she joined the Teen Titans and fought for justice against the forces of evil. She's strong, invulnerable, fires powerful energy blasts and can fly. She's also prone to misunderstanding humanity quite frequently, in part due to her alien upbringing and in part due to her naivete.
These misunderstandings would be more detrimental in the Marvel Universe where she lacks allies and a home. Starfire would quickly find herself on the wrong side of a lot of situations, particularly if she crossed Captain Marvel the wrong way.
2 Azrael
Jean-Paul Valley, regardless of the name he works under, has always held a place of instability in the DC Universe. Trained by the Order of St. Dumas as an assassin, it took Valley years to break free from their influence. He served as Batman when Bruce Wayne was out of commission but screwed that up when he went of the rails and almost burned Gotham to the ground to protect it.
Valley has walked the line between hero and villain pretty precariously since day one. In the Marvel Universe, he would be dragged across that line and inevitably end up in conflict with street level heroes like Daredevil.
1 Aquaman
Marvel already has one arrogant King of Atlantis to deal with. They definitely don't need two. Aquaman is a powerful hero and the leader of a dominant undersea nation. He stands with the Justice League in his world so he would most likely be inclined to do the same with the Avengers.
But once he saw how strained the relationship is between the surface world and Atlantis in the Marvel Universe, he would cross the line quite quickly. Defending Atlantis isn't an inherently villainous act but it would definitely put him at odds with Marvel's heroes, not to mention Namor.