I was told once that as long as the shot lands between the shirt pockets caliber doesn't mean much. Ok, I buy into that but what about bears, they don't wear shirts!
Shot placement is more important, but if given the option of hitting a bad guy's center mass with a .22LR or a 9mm, I'm going to choose 9mm.
If somebody goes for the last piece of pizza, would you rather hit them in the chest with a dollar store water gun or hit them in the hand with a frying pan?
Is the shooter a capable and competent shooter? If he/she is then I'd say shot placement. But if the shooter is not as accurate as the woman bear killer then I'd opt for a bigger gun. Are we pitchin pennies or throwing hand grenades?