give anyone kryptonite and they can beat supes. end of story. cap would own bats five thousand times over. batman's normal human body will wear out after time while cap's super-soldier body will keep going.
"HA! You wish. Bats is a way better fighter. If Bats can beat Superman and most other people more powerful than him then he could whup Cap no problem."
A few problems with that.
1) Batman has never beaten Superman. At most he's stalled him until Superman snapped out of mind-control or help arrived. Not to mention that Superman didn't even want to hurt Batman in those 'fights.'
2) Cap has also beaten foes more powerful than him. And he didn't need huge amounts of one-sided planning time, specialised equipment etc to do it.
3) Cap is one of the best fighters on Marvel Earth. I'd say he's a better fighter than Batman.