I’m not sure shot size is even a consideration. With plastic wads, the shot pattern, particularly out of any shotgun not choked straight cylinder (no choke at all), is less than about 6 inches at under 10 yards, so basically a slug of lead.
When I used to guide for pheasants and looked at thousands of hunting photos I took, other than head off the stock and feet all tangled up in the wrong position, the cause of most missed was shooting too close before the pattern had a chance to open up. I did a lot of pattern demonstrations and with a 12 gauge and modified choke, at 8-10 yards, the pattern was basically a single hole about 2-3 inches in diameter for the shot and another hole for the wad. And that was with 6 shot.
Also, while smaller shot does not keep the kinetic energy of larger shot (at that distance it doesn’t matter), it does penetrate soft tissue easier and deeper.
If the distance is over 10 yards, there is no need for deadly force because escape is possible. If the distance is less than 10 yards and there is a barrier, like a door or a window, something that requires heavier shot to breech, there is no need for deadly force because escape is possible.
The caveat would be if the other person is armed as well. Then all bets are off, but still not sure shot size matters at that point.