One plot idea could be that Superman is exposed to a new type of kryptonite that not only weakens him physically but also starts to affect his mind, making him a danger to himself and others. Batman, using his detective skills, discovers the source of this new kryptonite and figures out a way to neutralize it, thus saving Superman. Another could be that Superman is framed for a crime he didn't commit and is being hunted by the world. Batman, believing in his friend's innocence, uses his resources and stealth to clear Superman's name and save him from the wrath of the world.
Often it starts with mutual respect. They recognize each other's abilities and dedication to justice. For instance, Superman respects Batman's ability to fight crime without powers, and Batman respects Superman's selfless use of his powers.
One possible reason could be mind control. Maybe some villain has taken over Superman's mind and made him do it. Another reason might be a fundamental difference in their ideologies that has escalated to the point of no return.
Lois Lane is often a popular character. In fanfiction, she might play a crucial role in mediating between Batman and Superman or getting involved in their adventures in a more hands - on way, using her investigative journalism skills.
Alfred Pennyworth is quite popular too. He can offer his wisdom and support to Batman, and his interactions with Superman can be both humorous and heartwarming. He's like the glue that holds things together in the Batcave, and his presence can bring a sense of home to the story.
It's more modern in terms of art and storytelling. The New 52 version has a different aesthetic compared to older comics. It often has a faster - paced plot.
Lex Luthor is often an interesting character in such fanfictions. He might be the one pulling the strings behind the scenes, fueling Batman's distrust of Superman. Another could be Alfred. His wisdom and influence on Batman can add depth to the story. He might try to talk Batman out of fighting Superman or help him in a more covert way. And then there's Wonder Woman. She could be caught in the middle, trying to mediate between the two or having her own motives for getting involved in their conflict.
Catwoman can also be a popular character. She could be in a love - triangle situation with Batman, and her thieving ways might put her at odds with the female Superman who stands for truth and justice. There could be some really interesting interactions between the three of them, like Catwoman trying to steal a valuable item that the female Superman is protecting, while Batman is caught in the middle, not sure who to side with at first.
Wonder Woman could also be involved. She might be caught in the middle, trying to stop the fight at first. But if she realizes that Superman is being a threat for some reason, she could side with Batman, or at least not interfere in Batman's attempt to defeat Superman.
In many fanfictions, Jason saving Batman in 'Batman Arkham Knight' often shows a new side of their complex relationship. It could be a moment of redemption for Jason. Maybe he realizes the true meaning of Batman's mission and decides to put aside their differences. This scenario allows for deep character exploration.