If each has their weapons, then I'd say Batman most of the time. Batman has smoke and gas grenades (and a gas mask), small explosives, Batarangs, and a grapnel gun. Captain America has...a shield. Granted, an indestructible shield that he can use as a frisbee, but still a shield. Sure the standard batarang isn't very useful in this fight, but if Batman uses flash-bang, smoke, or sedative gas grenades, then Cap is disoriented and at a severe disadvantage, while Batman will be fine. His grapnel gun also provides Batman with far superior mobility to Captain America. Batman will probably know about Captain America's shield-throwing tactic, so he'll be prepared to dodge it, and I doubt that Batman will fall for the whole "hits him in the back of the head on return" trick.
On the other hand, if Captain America can keep his defense up with his shield, then the shield is much more useful for hand to hand combat than most of Batman's weapons. Batman has better body armor than Captain America, but Cap's shield more than makes up for the difference. However, the shield can only protect one side of the body, so if Batman can get around Captain America before he can react, then Bats should be able to get a few blows in.
Combine this together, and Batman is best advised to use a hit-and-run strategy, while Captain America will do best if he can keep close in with Batman.
Without weapons, it's a tough call. They're equal to each other, and they are both the top fighter of their respective universe, and the best tactician who serve as such for their universe's respective main superhero teams (the Justice League and Avengers/Ultimates, respectively). I'd say the deciding factor is the scenario and luck. Who has the environment advantage, and who gets the first blow, and who gets the best opportunities to strike where, and so on. It's an even match.
Thoughts on my analysis?
Originally Posted by Enriquespy
Welll its kinda like a ninja vesus a samurai Isn't it? I'd say Batman, just because I like him better. :P
Originally Posted by Franklin Richards
Howard Hughes VS Audie Murphy
Donald Trump VS Davy Crockett
Steve Jobs VS George Washington
I'll go with Captain America on this one.
I think you forgot about Batman being the top fighter and tactician in the DC Universe. In that regard, he is pretty much equivalent to Captain America, but with billions of dollars as well. Your analogy doesn't work.
Originally Posted by Duke
In terms of sheer strenght & ability i'd probably have to say Captain America due to the serum. Batman does have an edge on him on gadgets, vehicles, & cunning.
I don't think Captain America is superhuman. I know he lost the Super Soldier Serum once, and kept up his athletic build through training.
Vehicles aren't relevant because Batman's not going to run over Captain America.