Look I know that this is weak, but how else will this work?
In the trailer you hear Lex, mixed in with reputable sources (like Charlie Rose and Neil Degrasse Tyson), talking trash on Superman. Superman will probably reach out to Lex, "Hey I'm a good guy." Lex, if done properly, will be ready. He will then use red kryptonite on him and get evil Superman. Evil Superman will act out, as Jeremy Irons was describing, and Batman will step in. Batman will already have issues with Superman, given Superman's actions with killing someone(Zod) and destroying a city; which probably killed one of Bruce Wayne friends (from earlier scene leaks).
So Batman wants a piece of him already, then Superman starts acting crazy and Batman has no other choice than to strike;). I say this because @ 1:40 in the trailer Superman looks like he has a 5 o'clock shadow then you, purposly, don't see his face after that. He must be evil Superman.
Reasoning:
You can't have Superman beat up Batman, Superman would be a bully and that would sync up with Superman's image. Also, this would make older viewers feel appreciated by having a call back to previous Superman entries and give a legitimate reason to cheer for Batman vs Superman.