Cmon, let's not excuse the stupidity and laziness of how their pathetic fight was set up. First of all Superman shows no "dislike" for Batman at all. He's concerned but hardly "outraged" at what Batman is doing. And they hardly say a word to each other. Superman and Batman share the goddamn screen for the first time EVER and it's wasted on the dumbest dialogue possible that a in 6 year old could write.
"The Bat is dead, bury it"
"Do you bleed?"
Who writes this stuff? And the worst part of it all is Batman was chasing guys blowing all to before he was stopped but Superman just gives those guys a pass because they're obviously just having kicks on a Friday night, with mini-guns

And right before they fight Superman doesn't give two s about Batman. He doesn't care where Batman is. He doesn't care what Batman is doing. The only reason they fight is because Lex kidnaps Supe's mommy, gives him the villain monologue and forces him into it. There's no tension whatsoever. It's just two idiots fighting in the rain because Superman can't find the time or patience to get it through Batman's skull that he's being forced into this even though he has plenty of chances. The whole fight was set up in the most moronic way possible.