Think ballistics
Don't get hung up on the size of the bore; think pellet number, size, and velocity. For FEDERAL shotshells, by way of example..
12 gauge 3" magnum #00 buck 18 .33cal pellets 1210fps
20 gauge 3" magnum #2 buck 18 .27cal pellets 1200fps
Either way, that's a WHOLE bunch of energy dumped all at once into a target. Not much difference at the terminal end, and the 20 is easier for smaller shooters to shoot well.
MOLON LABE !
Oldragon