The 22 cal handgun is not known as a stopper. In 1957, in El Segundo, California, a perp (using a 22 cal snubby) shot 2 police officers, but before collapsing, one of the officers fired at the fleeing perp, hitting the perp in the shoulder. Both officers died at the scene. 47 years later the perp was caught, perhaps the oldest solved cold case on record.
That's the problem with the 22 cal handgun, even a shot the thru the heart can give the victim about 15 seconds to return fire, (in a gunfight 15 seconds is a long time) and for an instant stop an accurate head shot(s) is/are needed (ie Colorado Springs incident).
All things being equal, the small accurate 22 cal handgun can be superior to a small heavy recoiling 357 handgun ... only accurate hits count.
Now, to find a small accurate 22 cal handgun.
For 20 years the sea was my home, always recall the sun going down, and my trusty friend, a 1911 pistol, strapped to my side.