In BvS universe the setting ish not so dark one. This version the Batman like got personal vendetta against Superman like that and not just simply distrust and like aiming to kill him like that.
Beside the focus should be the conflicts and the mistrust between B and S, not like moobie still got Wonderman got Doomsday very extra stealing the limelight.
its just an adaptation, not a panel by panel shot of the comic universe mah
imo i feel bats didn't like supes initially is because of what is being explained in the movie, that he feels that supes doesnt know the consequences of his actions even though he is actually struggling with it, and that just because he got superpowers he can do anything he want.
actually there is a prequel comic to the bvs movie, and it was implied that bats is abit jealous of supes because bats has to work very hard to get to where he is while supes is born with it and doesnt have to work for it.
besides at the end of the movie, can tell that bats still doesnt trust supes, and that he knows that supes will come back because of the vision that flash showed him. hence he will be focusing on finding the rest of the metahumans in order to prepare for darkseid and eventually supes.