There's already been a really long thread on this one.
http://www.killermovies.com/forums/showthread.php?s=&threadid=19024
cap and batman in fighting abilities are at the same level. Cap sorum only put cap with the perfection of a human body just like bat has trained to reach it, and cap only have a shield, batman could use so more gadjets, for example some type of gas like he did, with spawn (altough spawn would and did kick his ass, no question about this one)
if the fight was only with punches and kicks i would say a tie.
IT can be seen in avengers v jla. I (batman) admit that the cap' will eventually best me in a fight.
"cap would destroy batman" - silversurfer66
very under studied
"This would be an epic battle. I would love to see it." - captain america
if it was a duke out to the end of one of the heroes then i fully agree with this.