1) I concede to the fighting advantage, it is dead even.
2)Batman is also considered peak human, he is just a better acrobat, for the same reasons you listed.
3)What you consider peak Human and what Marvel considers peak human is obviously not the same. Marvel puts Cap at an 800 pound bench, not 1 ton! Also his Bat's strength is more spread out, thus his better agility.
4)Batman has plenty of endurance, what you consider a long drawn out fight might not be as long as you think it is.
5)I agree on both counts.
6)Hmm, are you beggining to waver? Cap wouldn't appreciate that. Fine, they're both equal strategist, I can't prove otherwise. But one of Bat's more subtle advantages is his ability to use what he's learned from his villians, something that Cap might spit at but would prove quite dangerous. And Bats has only had his comic for how long?
7)Intellegence obviously goes to Batman. Please do note that I said this is not likely to have an effect on the outcome, unless a situation arises which would prove advantageous. Cap is the better leader, something that won't help him in this fight, all your points hear is his strategy and leadership, not intellegence.
8)BP is by you admittedly a bad example so i'll leave it alone.