Let's utilize logic, shall we? And who better than me, Mr. Rational.
If the world were to be reduced to a level of degradation such as the one mentioned here in this thread, then we can assume that the majority of its humanoid inhabitants would be split between zombies and vampires. A simple examination of the two should prove fruitful in settling this matter.
Zombies. Depending on the film, they can be slow or fast moving. The majority of films have them as slow and lethargic. They possess no rational thinking, rarely use tools, and can generally be outwitted by a quick thinking racoon. Their only purpose involves personal gratification through the eating of human flesh.
Vampires. Smart, strong, and capable of every human function, excluding tanning. They are able to utilize weapons and are capable of rational thinking. Their purpose in life differs from film to film, but generally speaking they exist to survive as a species and to experience a sense of personal gratification..
The Verdict. Although vampires would find it difficult to survive without a fresh supply of normal human blood, they would easily dominate the sluggish and dim-witted zombies. Additionally, having a piece of flesh bitten away from an appendage and the related infection incurred from zombie saliva are not included in the list of things that threaten a vampires life. Vampires win.