Now that you mention it, Batman wanting to make Superman bleed seems a little out of character.
The reason for it, most likely, is that the creative team behind Dawn of Justice want to recreate the classic confrontation at the end of The Dark Knight Returns, Batman’s power suit and all.
The reason why that fight worked not just on its own, but as the climax of that story, was because it’s based on the entire history of the characters and their relationship. Both are friends with the same goals, but very different ideologies regarding how to achieve them. In the story, Batman is the ultimate libertarian crusader and Superman is the errand boy for the United States President. Their fight plays as both an inevitable conflict, but also a tragedy that it happened at all. If you re-read the fight, the entire time Superman is holding back and pleading with Bruce to stop, which explains why he isn’t killing him instantly. Bruce, on the other hand, knows that the fight is important to further his goals and embraces it… but not by killing Clark. Instead, Batman fakes his own death during the fight after gaining the upper hand because he never wanted to hurt Clark for its own sake, but rather make a statement about the effectiveness of his methods through beating the poster boy for government.
Now, it’s very possible they’ll play up the libertarian and government angles, but they are missing a key element that made the relationship work: in the current film, Superman and Batman are not friends. In fact, the implication for the trailer seems to be they actively hate each other. Therefore, there’s very little reason, power suit or no, Superman couldn’t instantly take Batman out. Superman could use his laser eyes to fry his legs off, throw him into orbit, or bring back the classic and snap his neck. Even in the Hush arc, when Batman fought Superman he based his strategy to Superman not wanting to hurt him despite being under Poison Ivy’s influence.
Yet it seems they do want to hurt each other. Why?
We don’t know for sure yet. The trailer seems to imply that Superman has become an (understandably) controversial figure after Man of Steel. Some people worship him, while others are weary of him. Batman seems to downright hate him. If the rumors are true, that hate at least partially comes from Metropolis being trashed, which makes perfect sense.
But Superman obviously isn’t going to kill Batman.
Of course, which, in a way, makes the entire conflict disingenuous. Superman can’t kill Batman and vice versa, thus negating any dramatic stakes for the fight. In addition, because they lack any history in the story their fight has no emotion to it. The whole driving force ends up feeling like they want Batman to fight Superman because it’s cool, which it is, but when you’re telling a story the cool factor can’t be the only driving force, especially when that conflict will have to fizzle out at some point. After all, these guys have to form the Justice League, so by the end of the movie they’re going to have to become at least allies…