I would like to prove Skarin wrong. Versus matches can be very thought provoking. So, here we go.
In terms of general fighting, I would say that the zombies would eventually win. Reasons you say? Nazis would operate as all teams operate...you look for what the enemy is wearing and don't shoot the guys wearing the same thing as you. But if your friend Nazi Ned is bitten by a zombie and stumbles up to you, you may not even blink. Zombies are harder to kill than Nazis. Bullets kill Nazis, but destruction of the brain only kills zombies. Therefore, gas chambers are ineffective against zombies, as are scare tactics. If any outside forces (come on, there are always outside forces) join the battle, then let's face it, everyone hates Nazis and zombies, so both teams will be attacked, but the Nazis will die easier. The Nazi army is made of a specific group of people. They don't recruit outside the "arian race" so their numbers are set. The zombie army is ever-growing. By-standers join, teammates join, and they just keep coming. Game, set, match...zombies win.
Now who do I want to win? Nazis. As much as I hate them like everyone else does, they are less of a global threat and can be dealt with easier. If the Nazis win, then we just have to go back and whoop them like in WWII. If the zombies win, it will spread like the disease it is, and the pandemic will eventually kill off mankind. That's a simple case of who you'd rather face in the dust trailing their epic battle.