Originally Posted by The Question
Captain America trains regularly, and is a very highly skilled hand to hand combatant. Cap is also highly inteligent, and I don't see why Batman is automatically moreso. Also, I must add: Knowing more techniques and fighting styles does not make you a better fighter. It just means you're very anal retentive about learning everything you can. Experience and a quick mind are what wins fights, not moves.
I guess it comes down to a matter of opinion about who would defeat who, but you can't possibly argue the intellect or martial-arts skills of Captain America vs Batamn, it's just so one-sided. Bruce Wayne spent 12 years of his life mastering over 100 different martial-arts styles. That makes for an unpredictably overwhelming opponent in hand-to-hand combat.
As far as smarts go, Batman is one of the most keen minds on the face of the planet. This is a guy who could solve a crime committed in Cleveland with a q-tip from a cabinet in Honolulu. The whole super-genius bit is part of his character, bats are highly intelligent for their brain size and animal species. Only men like Reed Richards, Bruce Banner or Hank Pym are up in that class of genius. Cap isn't even in the same league.