It depends which documentary is correct.
In Resident Evil severe trauma to the brain could cause the deanimation of a zombie. At least one
died redied from striking it's head against a wall after being forcefully kicked. In this case I think the 9mm would be adequate.
However in most of the other documentaries the brain must be destroyed, The extra KE of the 5.56 gives it a decided advantage here. Therefore the 5.56 is the way to go. Also the 5.56 as a slight advantage in weight. IMHO it is easier to handle to do it's length (more to hold on to).
For zombies I'd go with M193. While a soft point will usually be able to penetrate the skull, I want the extra insurance of FMJ to penetrate bone and destroy grey matter.
ETA: Just reread the comments about the 22lr. I have a couple of 22s and a couple bricks of ammo. But I'm not sure how much I trust a 22 to reliably penetrate the skull. Also the documentaries are often unclear as to just how much of the brain must be destroyed to deanimate a zombie. Therefore there is a risk that even a perfect head shot could leave enough of the zombie's brain intact to allow them to remain animated.
ps I really love zombie threads