What DeM said... also, turn it around; why does punching a hole in someone kill them? A lot depends on where you do it, but basically it's either mechanical destruction of the nervous system or loss of blood, aka shock. Keep the blood from leaking, patch the sucking chest wound, and you've got a fighting chance. After that comes the long-term fight against infection and so forth, which doesn't apply to a discussion of "stopping power."
With a full-metal jacket 9mm, you very well may NOT dump the entire load of energy on the target -- you may get a "darning needle" through-and-through wound, and waste 80% of that energy on the wall behind it. (Or an innocent bystander... I hate reckless punks as much as anyone else does.)
A big slow .45 round is a better stopper than a sharp-barking 9mm because there's a much better chance the guy you're trying to stop* will get the full effect. That's also why a hollowpoint is MORALLY superior to a round-nose; shooting someone once -- and stopping the fight -- actually gives them a better chance of surviving than shooting them nine times (because they didn't quit after the first one).
*Not kill, not murder -- we're talking about the legal and moral need to stop someone who is committing murder. I don't joke around on that subject. Nor do I take fiendish glee in it. Dropping virtual orbiting anvils is one thing; dropping a real hammer on a real criminal is another.