You -do- realize that Marvel vs. DC was literally a popularity contest that they wrote the story around, correct? In other words, they sent out little ballots to a bunch of comic shops, fans voted, and then they wrote the story (and the victors) according to who got the most votes. This is why Storm is able to defeat Wonder Woman, and (no adamantium!) Wolverine is able to "defeat" Lobo (in a contest so lopsided they couldn't even find a way to justifiably show it on-panel).
So yeah, no surprise Batman beat Captain America there. Batman is more popular than Captain America.