I know this is an oldie but a goodie, and that my answer won’t be much different than any other answer out there, but here’s my two-cents on the subject.
First off, we need to know what kind of zombie we are talking about. Obviously, a normal person in a trance isn’t going to do a damn thing to a vampire. Are we talking about a victim of severe rabies or other debilitating disease? Dawn of the Dead/ The Walking Dead “Classic zombie”?
We have to remember that a vampire is one of the undead. It’s essentially a walking corpse already. Therefore, in my opinion, a zombie biting a vampire is either going to piss the vampire off off or make him/her laugh.
If a vampire were to bite a zombie, it would all depend again on what kind of zombie it was. I don’t think the shambling, missing-limbs-version would benefit much from a vampire bite, but the human in the trance would be the next vampire-in-the-making.
I know there are a lot of people who think I’m wrong for whatever reason, but seriously. There’s not much you can do to a vampire!