This is mostly true in common scenarios faced in civilian self defense shootings.Forget all the nonsense that one caliber is far superior to others. When it comes down to when shooting a person with a hand gun NOTHING is more important than shot placement. As Greg Ellifritz said after producing a study of shootings over a 10 year period hand gun stopping power stinks, use a rifle or a shotgun.
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HOWEVER, I believe that when you consider performance when penetrating barriers like autoglass, vehicle panels, doors, furniture and other objects there is often a significant difference between something like a .380 or .38sp and 9mm, 40 cal or 357.
Will you have to shoot through a barrier in your hypothetical self defense scenario? Probably not... but who knows.
Maybe you're in a restaurant and have to shoot through a booth or pane of glass. Maybe you're in your vehicle and have to shoot through the door. Perhaps you're in your home and you have to shoot through drywall.
All outside chances and certainly not the 'norm', but certainly worth considering. I believe Paul Harrel has a video out there where in a test .380 caliber bullets only penetrated a vehicle door about 50% of the time at a relatively short range.
With that said, I carry a .380 pistol quite often. Is it the most effective firepower? Absolutely not, but by carrying a pistol instead of a rifle I'm kind of already sacrificing power for concealment. Sacrificing a bit of barrier penetration for substantial increases in concealment is something I can live with. If it leaves me dead in the streets then so be it, at least I tried... and god willing there will be an empty pile of brass around me.