Nothing would happen. They are both undead (so technically Vampires are zombies, in a way).
If you've ever read Dracula you see that you don't become a Vampire until you die from blood-loss or whatever you die from. It's a curse, whereas the Zombie thing is more of a disease. Vampires can't get diseased.
I don't know why I decided to geek out so hard on this. I guess I just felt like it.
Exactly. It would be like a bump on the shoulder. The vampire would appologize (because they have intelligence) and the zombie would just look at the vampire and go "UUUUHHHHHHHHHHHHHH."
actually, since the vampire is dead and has no blood flow, there would be no way for the zombie virus to spread and change the vampire in any way, same with zombie. so, nothing.