As a law enforcement firearms instructor for over 31 years, I can say I have been at all ends of this debate. After 31 years I have come to the conclusion that with a handgun, it's only effective with proper bullet placement.
No "magic bullet" is going to turn a bad hit into a fight stopper. No matter what caliber you carry, you still have to get good center of available mass hits to stop a person. I advise my students to carry the weapon and the round that you can shoot the best with. If you can put a good standard response two round group on a target with a .45ACP, great. If you can't, but you can with a 9mm, then that's the weapon you should carry.
We carry handguns because most of the time, a rifle or a shotgun, are either to difficult or inappropriate to carry. If we knew exactly when we were going to be involved in a gunfight, we'd carry that rifle or shotgun. Since we don't, a handgun usually is the correct choice. And being able to reliably hit your target cold and on demand, is the key to surviving an armed encounter.