To me, two of the most fascinating zombie movies are Day of the Dead and Shaun of the Dead. They're smart movies, each with totally a different affect or feel. They balance horror and humor on quite opposite ends of an experiential spectrum. Day of the Dead is a great horror movie (perhaps Romero's best, in my opinion, next to the original Night of the Living Dead), and Shaun of the Dead is laugh out loud funny, but they also share an important similarity. They ask about this imagined zombie weltkrieg: “What do we do when zombies start acting like normal people?”
Admittedly, Day of the Dead as a scenario has more to do with the question of how we get zombies to be civilized people than what we do when they are civilized. The civilized zombie is in the minority, which is sort of terrifying when one considers zombies as people, but momentum builds toward civilization and the acceptance of the formerly non-human human people as people. I think we can take the doctor's method (“They have to be rewarded...”) as a constant. If they had been re-civilized, zombies could be treated as equal citizens, but then anti-zombie prejudice and ignorance from militant white men with guns means there must be blood everywhere before that can happen.
Shaun of the Dead raises human/zombie normality issues pretty constantly. The whole beginning of the movie relies on human/zombie similarity. It provides most of the gags. I think you could say it's a theme of the movie. The ending, especially, explores the idea of how to civilize zombies-- hilariously.
Unfortunately, neither movie seems to address the question of zombie personhood in the long-term. It is interesting, though, that such long-term thinking drives the scientists in Day of the Dead to start re-educating zombies in the first place. However, they both look at the most important aspect of the global undead revolt myth: what happens when it is no longer a war?