The only thing I've killed with a handgun was a large porcupine.
I Put 5 rounds of .45 hollowpoint into the center of mass, and it still took several minutes for the thing to die. It was moving briskly for at least 45 seconds to a minute.
When it finally did die, I flipped it over, and all 5 shots had penetrated, expanded, and left nasty exit wounds through the chest cavity.
I put the 6th round into it's head, but it bounced off its skull, without even phasing the porcupine.
Now this was under no stress (I had to shoot it, or the dogs would go after it), I was in no personal danger. Shot placement was into vital areas, and the ammo performed as designed.
After that episode I seriously had to sit down and reconsider what would make me feel safe facing a grizzly. If a bear had half the constitution of that porcupine, I would be in a world of hurt.
I'm sure a .44 would eventually kill a griz, provided the right shots were made, and enough of them, but don't expect one to instantly drop when it realizes it's just been shot.