Okay, for the even numbers scenario... The vampires would certainly have a bit of competition within their ranks, but all of that would soon sort itself out as the most powerful and capable vampires rose to the top and established a complex hierarchy.
Once that happened, though, the zombies would indeed be at the vampires' doorstep.
The vampires would have to all scatter to different locations in order to preserve their undeaths. This would lead to, like Janus Vesta said, guerrilla warfare on the vampires' part. The vampires would pick off zombies with several cool vampire weapons and soon herd the zombies into a small, isolated area. From there, the vampires would drop a wonderful tactical nuclear bomb on the zombies, obliterating them.
EDIT: Now, if the human population was still as large as it is now, like L1250 said, it would really liven things up. The humans could be one of three things to the vampires/zombies:
1: A commodity that both undead sides fight over
2: Allies for the vampires (who would ever want to ally with zombies?!)
3: Enemies of both undead species, trying to preserve the human way of life
If the humans were a commodity, the vampires would most likely, as Amnestic said, corral them and use them for a source of blood before the zombies could lumber over and infect said humans. The vampires could also be incredibly callous and use the humans that they have drained for cannon fodder to fend off the zombies. If the zombies got the humans, however, they would make more zombies, leading to much greater zombie numbers.
I shall discuss the next 2 scenarios in future posts.
(This is really fun! Should we ask a mod to put this in the RP forum?)