Superman and Batman are pretty much equally my favorite, would be interested in seeing Batman become more violent which is likely what would happen to him. In the comics, he shows he is willing to break his code and kill for Nightwing, or if he's really pissed. In the war of jokes and riddles, he legitimately tries to stab the Riddler and beats Deadshot within an inch of his life, in Forever Evil he almost strangles Lex to death because he thinks he is hurting Nightwing, he also recently breaks KG Beast's neck and leaves him to freeze to death over Nightwing. In the Injustice universe, Nightwing is dead and killed by his own son. I have read almost every Batman comic in the main DC continuity post Flashpoint and I genuinely think this would break him beyond repair, maybe not full blown evil, but closer to the Ben Affleck Batman or the Dark Knight Returns Batman. In Injustice it's basically just peak Batman kicking everyone's ass and being at the top of his game.
Real missed opportunity for Batman to not have an "I get it" moment with Superman. It is also out of character for Superman to be broken FOREVER over Lois, I have also read a fair bit of Superman and Justice League, I don't think he would be THIS evil. Basically, it is more plausible that Batman and Superman would eventually choose to work together as borderline dictators.