Alright, now while my opponent has done some ridiculously good debating on behalf of Captain America, I still firmly believe this is Bruce's fight to lose, if the gap between them is so small it's practically nonexistent. Batman, while not on Cap's level physically, is perfectly capable of contending with Rogers' enhanced human physicals utilizing a combination of his highly impressive peak human physicals and his superior skill. While true, he has struggled against guys like Azrael (on occassion - he's had mixed showings) and Deathstroke, it's worth noting that neither of these guys are Captain America and Bruce didn't utilize tech or stealth as he's been shown to use in plenty of other fights. Cap's adaptability in combat is something Bruce has shown he can keep up with, as evidenced by his fights with Cassandra Cain (who has the ability to read the moves of her opponent and can also copy their moves, much like Taskmaster) and Philo Zeiss, a guy will full-blown metahuman senses who viewed the world in slow motion and has already studied Batman, yet he was totally unable to beat the Dark Knight. In terms of tactical skill, Bruce has formed complex, multi-layered plans while in combat, analysed and figured out the weaknesses in an opponent that was blocking the Flash's movement, he's recognized styles with a glance and spends practically every moment of a fight studying his opponent, figuring out their strategy and finding ways to win. On top of that, his vast wealth of gear ensures that he'll always have something to surprise Cap with, whether it be a grenades, smoke, a taser, grapple gun, tranquilizers, liquid nitrogen pellets or any one of the magnificent toys Bruce has in his belt (it's worth noting two examples you used in your last post for gear are of the New 52 and aren't applicable). Furthermore, it's worth noting that Bruce simply has a major wildcard to fall back on, with stealth. If he begins to feel pressured by Cap's assault, he can adjust his strategy and go ninja mode, striking Cap from the shadows with everything he's got and wearing him down for the victory. While the shield my be trouble, Bruce is certainly fast enough to dodge it, note the trajectory and remove it from play using a grapple gun or another such gadget. Cap might have the ability to use his shield to crash through trucks, but being the outstanding pillar of virtue that he is, he'd never use it.
Overall, I think Bruce simply has a wider array of ways to win besides simply beating his opponent into submission and he's got the intelligence to use them when the chips are down. If they fought 100 times, honestly, I think it may come down to Bruce winning 51/100, that's how close the fight is and I think we've done our best to portray it that way.