Cap would win because he is faster, stronger, no disease can affect him, he can endure all climate, his mind set is on war, he's a master planner, and he's an amazing fighter. None of batman's weapons can get through Cap's shield.(that's just some of the facts)
Batman is also very powerful he has a mass array of weapons and he could easily take on Captain America. If I may make a recommendation one of us should download the Software from "Deadliest Warrior" and enter in there stats and X-factors. I accept our challenge.
Batman is no where near the power of cap. Plus cap is great in any environment so, any where he would break him. Also one hit from cap's shield and a normal person would die.(such as Batman)Proof on that is on deadliest warrior, when a spartan shield would kill any person.