Approximately a year ago I read of a similar incident to the one described by doublebase that occurred in Jackson, MS. After a car chase, a cop was shot by the perp with a .25 from a distance of about 40 yards. The cop was off duty, in route home from a training session, and was not wearing his vest. As he sat at an intersection waiting for the light to change he seen a car go by that had just been taken in a carjacking. Off-duty, but in his patrol car he attempted to stop the car. After wrecking the car, the perp exited the vehicle through the driver's side window, turned and shot one time hitting the policeman in the lower part of his stomach. The cop returned fire with his service .40 hitting the perp three times. The cop died on the spot, (bled to death) while the perp survived and fully recovered from his wounds.
I also sat on a jury several years ago where a woman shot her common law husband, killing him. He was an abuser, and had beat her earlier that night and left. When he returned and attempted to beat her again she ran into the bedroom, picked up a single-shot .22 Butler derringer loaded with one .22 short. She turned and fired hitting the man in the left eye. The bullet entered the brain cavity and bounced around turning it into mush. He was dead on the spot.
The point is, anyone can get lucky with a small gun, and often there are extenuating circumstances where people walk away, even after being shot numerous times with a big bore gun. But by enlarge, the majority of the time the .22 and .25 are ineffective while the big bores normally render a perp down and out.