Since Zombies are loosely based on African, Haitian, and U.S. southern folklore, the sci-fi / horror zombies are based on their real counterparts, which are quite slow.
The witch-doctor extracts a tetrodotoxin from a puffer-fish—which is mixed with a powder and mixed with dirt—the powder is called ‘goofer dust’ It is spread where the victim is likely to touch—in the dirt just outside his door, or on the door itself, etc.
The tetrodotoxin causes the one effected to become paralyzed appear to die—the breathing and pulse are extremely slow. Of course, the Zombie does not actually DIE but appears to—modern techniques could reveal that the person is not fully dead. This lack of oxygen (or lack of oxygen from being buried several days) does extensive brain damage.
The ‘zombie’ is able to follow simple instructions such as agricultural work or simple menial tasks—but basically lives in a slow stupor and is not very coherent. Occasionally, several years later someone recognizes them (as someone who supposedly died) even if the person is rescued there is extensive brain damage,
Sci-Fi zombies are based on this real counterpart but usually are affected by a virus, or alien entity inhabiting the body. It just seems like death and decay would slow the brain function.
Also, I do not know how much truth there is to ‘real’ zombie phenomenon—Voodoo is common in the region in which I live (I studied it as a project for a folklore class) and I know an African American church that deals with it—which is mostly the power of suggestion. Christian missionaries in the Caribbean and Central America encounter it occasionally.