you don't hold your own against korvac on skill either.....a shield, will power and a little pis are all needed.
as for skill--i'd say bats was slightly more skilled, but the difference is negligible. more mention is made of batman's skills, of all the ma he is trained in, how many weapons he is proficient with. there are 2 many examples of him fighting skilled opponents and dealing with them. cap has been shown to be below people like mantis and moondragon, while bruce contends well with guys like val. even logan has appeared to be more skilled than him in one scenario. all that said, i STILL think the skill levels are very close, but it think it is easier to support the stance that bat's is the more skilled, than the other way around.
regardless, this isn't the thread for this discussion--there is already a 200+ page thread that deals with bats vs cap no equipment.
on topic, their peak strength levels are nearly identical based on feats, with an edge to cap in a general sense.