I think they'll probably have Batman wary of Superman after the number the Kryptonians did on Metropolis. In the comics he's already planning how to bring down Superman the second he heard about him, probably will be the same. Eventually they'll team up.
In the end Lex Luthor will have gotten Kryptonite and have Superman as good as dead before Batman saves the day. Mark my words it'll be something like that.
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Well it wouldn't be surprising. I mean Batman's trying to make Gotham a better place to live, succeeds even , and then boom you have these super powerful aliens killing everyone in Metropolis.