Batman is a human, his power level is at Peak human capacity.
Captain America is beyond human capacity he is a low level metahuman. He is also probably the very best at this power level just like Batman is the very best at his.
Captain America have a powerful shield this weapon is beyond the best weapon Batman can come up with.
Captain America will be victorious in this battle not very easy but he will. who is the more popular and got more fans is another question !