Zombies can move about 30 feet every 6 seconds, which is kinda fast.
Either is fine so long as it fits the movie/game/whatever.
Slow shambling zombies shouldn't be left behind by more modern instalments, but there is room to share.
Zombie purists are a bit silly. I read a post that someone wasn't going to get L4D because they weren't true zombies. Sure whatever, but it was a pretty long post/whinge.
By all means have your preference but geez, just be happy that zombie lore hasn't been as raped as vampires have.