Fast zombies! Slow zombies!
I've read a few articles that discussed the entertainment value of each and found that people are way too serious about discussing this topic. 
This seems to have been a topic of conversation pretty much ever since zombie movies started being made.
The first zombie movie as far as I know was White Zombie in 1936 starring none other than the famous Béla Lugosi. This movie portrayed zombies in the most traditional sense. Using a magic potion Lugosi's character, Murder Legendre , a white Haitian voodoo master, kills people, revives them as zombies, and uses them as slaves in his sugar cane mill. 
These kind of zombies are just like normal people in that they can walk, talk, and do things as any living person might with the exception that they are enthralled by the voodoo master. Soulless beings, they have no sense of self.
|Just George Romero and his zombies|
It wasn't until 2002, I believe, that movie makers came up with a good "fast zombie" story. 28 Days Later was a freakin' awesome end of the world story. But it was also the end of zombies as we know it. These zombies weren't dead! They just got sick. They caught a virus and went buh-zerk. The virus turned people into killing machines. Only those that survived the attack and happened to be infected actually turned into zombies. The only mystery here is why they don't attack each other.
That's actually a classic trope across the entire genre. Zombies are totally on the same team. And they know each other! They look at each other like, "Uhnn. Hey."
So what makes a "proper" zombie? In my humble opinion it's pretty simple. True zombies are dead. They are supernatural and mysterious in origin. You can only turn zombie when bitten. Zombies move only as fast as their damaged rotting limbs will allow; and they can be "killed" only by destroying the brain. 
|It's zombie Jenga!|
I shall refrain from discussing the zombies in the comic books & AMC series The Walking Dead. It's an awesome new take on all things zombie and because it's still kind of new, there are people that haven't experienced it yet, that will, and I don't want to ruin it for them.
So, with that I'll leave my opinion.  Zombies, fast or slow, are dead and supernatural. If you zombify by catching a cold, you are sick, not a zombie.
And that settles that.