If we couch this in terms of their respective backstories, Bats should be superior in terms of versatility and knowledge of technique since he spent his formative years traveling the world to acquire his skill sets. Cap, by contrast, shouldn't know as much, since his origin indicates only extensive military/commando type fight training.
In terms of physical ability, Cap wins because he's been augmented to human perfection via the super-soldier serum. By the way, I'm assuming we're talking about traditional Cap and not Ultimate Cap, who can lift a couple of tons.
The result? In an ultimate fighting cage match, its close, but I say Bats wins by drawing on a superior portfolio of fighting skills. Despite all arguments based on previous fights or various feats performed by either character, the fact remains, that if one stays consistent with these characters' back stories, there is no way Captain America can be as knowledgeable as the Batman. No way. Plus, I also give Batman the edge in terms of sheer willpower. Although Cap is no slouch in this department either, I don't see him staring down the Batman and winning. Plus, Batman is dirtier. If push came to shove, Batman would gouge out Cap's eyes as soon as blink. I don't think Cap is up to that type of tactic.
If this fight takes place in any locale that allows the Batman to hide or or take advantage of cover, its not close. Cap is dead before he knows what hits him.