As someone who loves both universes of heroes, I sadly must admit that batman would lose. Caps abilities alone would put him ahead of the race and I'll tell you why. Batman has many skills and talents but at the end of the day he is not called "the super soldier of the century". Let's not forget that Caps ability improved his intellect and with can easily adapt in battles against his foes aside from the fact he doesn't have little to no weaknesses. Batman, although being one of the greatest heroes in the DC universe in my opinion, is limited with his abilities.