Re: Captain America vs Batman
Batman has taken out other more powerful people (like Bane, I won't be touching the Superman issue, since it seems to bring out the worst in people) and he has taken out several at the same time, but the same could be said for Cap. I dunno.
I am a huge Batman fanboy, so I would tend to say Batman, but I also like Cap a lot and I am aware that in the Marvel U he is somewhat an equivalent to Bruce, in terms of effectiveness and reliability, so... its not clear cut.
I could bring up the fact that Bruce beat him in the "vs." crossover, but only slightly and I could bring up that Bruce admitted that Cap could beat him, but that it would take him a long time to do so, in JLA/Avengers.
I think "could" is a good jumping off point. Yeah, Cap could beat Batman, but it also could go either way.
When I put fanboyism aside, I would say out of 10 battles, each would win 5, or Batman would win 6 out of 10, with a bit of luck.
Sure, Caps power and speed give him an advantage, but only a slight one, since Bruce isn't that far off. I would argue that Bane is stronger than Cap and Bruce did beat a fully roided Bane several times. Still, its an advantage for Cap.
On Bruces side, I would say that he is a bit more ruthless than Cap and overall much smarter. Caps no dummy, but we are talking about Bruce Wayne here, who builds a lot of his own gadgetry and vehicles in his spare time (after stopping an Arkham outbreak or something like that). He's also a master detective and has a genius level intellect, not much far behind the likes of Lex Luther or Tony Stark, on which level Cap surely isn't.
So, to be honest, Batman wouldn't need that much prep time, to take someone out... he would prep on the fly, while fighting. Thats what makes him that dangerous.
On martial arts prowess, I would say Bruce has a slight advantage, but that could be wrong, since I have read nearly everything Batman related since the 80s and only Caps most famous runs.
Batman is a polymath, mentally not operating on the same wavelength as the rest of us. In some Batman origin stories, they say he was a martial arts prodigy, who mastered all known forms of unarmed combat, with only 1 year of training each. Not became "very good at" or "reached 10th dan levels" at; mastered. So, I think thats more than Cap.