ZM Provides a nice first person experience for the humans while one player gets to be the ZM and RTS it up. It's fun to try to get through it all and kill zombies. Though you're not playing against actual people, just AI. This allows for some fun trap maps and death runs. The almost infinite amount of zombies can be pretty entertaining too, though as everyone knows, once your dead, your out.
ZPS is still zombies, but the zombies are other humans that have died, minus whitey. It's all FPS, so the zombies can't see where the humans are. They only know what they knew before dying, then they go to get their team mates. When players die in ZM, they sit in spectate, when players die in ZPS, they get to eat brains. The guns and weapons seem smoother to me in ZPS.. Graphics are nicer too.