Zombies Vs Vampires, who would win?

With the werewolves triumphant, could a zombie beat a vampire?

Though zombies have been fairly static over the years, variations being mostly, can they run or not. Vampires on the other hand, change wildly, some turn into bats, some into giant bat like humans, some just walk around shirtless.

I however, think under most types of vampires, the zombies would still win, as the vampires always require fresh blood, which zombies cannot provide.

Thoughts? Votes?