Batman would win, but would then have to face the rest of the Avengers. If Batman were defeated, nobody would know about it because he would have kept the entire thing a secret. All the brains in the world are of minimal use when you have Iron Man, the Hulk,, Thor, Ant Man,,, and whoever else is a part of the Legion today all angry at you.

I gotta give it up to Batman, even if it's Dick as Batman, and especially if it's Bucky as Cap. So Bucky's the one with the pistol! A gun is a coward's weapon, and Batman, in any incarnation, knows as few as 7 ways to defeat an armed assailant unarmed. Three of them are lethal, three are almost completely painless, and the seventh hurts like all hell.

I think the one you are thinkinf of is the issues where JLA and Avengers team up. That was when Superman aquired them during the final fight with Krona.

The one MR Khan is referring to I believe is the "DC vs Marvel Comics".

Batman is dependent upon his utility belt, that it is hard to say in a fight, that he would be able to beat Captain America, assuming it is just one on one.  The problem when you decide to make it more than just one on one fighting, and allow devices and so on, is that you get to bring in a bunch of unknowns into the mix.  

The rules were no rules of engagement, all weapons allowed but no preparation (basically they were made aware that they could be fighting soon, but they didn't know who they were meant to fight, and they didn't know when they would be summoned or where they would be summoned to), so Batman was allowed to have his utility belt, but couldn't make special preparations against Captain America specifically, or account for the fact that they would fight in a sewer, as they did

Batman by far...he's way smarter than Cpt. America,and has different accessories/resources at his disposal.

I would say that Batman would have to fight dirty, or he would have problems.  Straight one on one, Batman has issues against Cap.  So, it would depend on how things break down in the environment.  You then end up with the ability to improv vs raw capabilities.  If there was prep, then Batman would out prepare Captain America, but based on raw capabilities, it isn't easy at all to pick here.  For one thing, as much as Batman is prepared, Captain America isn't even in his universe and I doubt that he would even know how to handle the material made out of Cap's shield, because it doesn't exist in his universe.

@ richardhutnik: There's an easy solution for the shield as far as Batman is concerned: take the shield out of the equation by disrupting its flight pattern. That way, he can either blow him to smithereens with a plastic explosive, or, if he wants to make it a fair fight, he could forgo his utility belt entirely, and use martial arts because we all know that Batman, in any incarnation, is the superior martial artist. Hell, if it's Bucky as Cap, he'd probably be smart to go with the martial arts because, as I have stated before, Batman knows as few as 7 ways to deal with an armed assailant without weapons or gadgets.

Edit: And by the way, using stealth and "fighting dirty" are two very different things. In fact, the only time I've ever seen Batman "fight dirty" in any comic book when Bruce Wayne was behind the mask was during Batman: The Dark Knight Returns when he fought the Mutant Leader for the last time, and that was only because they were both in a cesspool, waist-deep in mud and feces.

I wasn't saying that the Shield would ever be thrown.  But it could be used as an instrument to bash, and is there any indication Atomantium and Vibranium could be blown up with plastic explosives, or that Captain America would bother throwing it? Those two don't exist in the universe of Batman, and are far more durable than you give credit FOR.  Or, how the heck do you think that Batman is going to get plastic explosives on Captain America.

And, I think if you start to remove devices and other means from preparation, you end up weakening Batman.  If it involved one on one, with time to prepare and bring anything into the ring, I would give the nod to Batman, because preparation is one of his major strengths.  However, in straight up brawling, then it tips the way of Captain America.  Unarmed, Batman is at a disadvantage, and it doesn't matter if Batman is superior at martial arts.

And "fighting dirty" means to take the fight onto a playing field which puts Captain America at a disadvantage, normally through the use of devices.  Batman's big thing is to tip the playing field to his advantage, through preparation.

On this note, I give you two bits of video evidence for what I am saying:

http://www.youtube.com/watch?v=FywMOuMqNuI

http://www.youtube.com/watch?v=PeT1t0lQn5Q

Please ID the scenario in which the two will be fighting? In a straight out 1v1 fight in an arena, Captain will win, he is a super soldier for a reason, and no matter how much body armour or gizmos Batman wears, he won't be able to compensate for the severe physical difference.

In a real world fight scenario, Captain A doesn't stand a chance.