Some zombies are sturdier than others.  In my opinion it’s kind of a sliding scale.

On the one side you have zombies from Fulci’s “Zombie 2.”  These are zombies that are so slow and weak that a teenager with a six pack of redbull and a hammer could have stopped that zombie apocalypse.  Now on the other side of the zombie toughness spectrum you have the zombies from “Return of the Living Dead.”  Fast, smart, and damned near unkillable save by total body immolation.  Even then that would just make the problem worse by spreading the Trioxin gas.

The other thing that made those zombies scary is that if you chop off random body parts, even those body parts keep coming after you…. Just like grandma.  (Shudder)