It's a bit of a vast and wide ranging question.
So, lets look at the 12 bore. Obviously the shotgun is for short range killing, under 50 yards but the shot can travel up to and over 300 yards. It takes time to learn the skills for moving targets but obviously cage trapped animals are easy targets.
For simplicity the smaller the shot size the greater the killing potential, size 8 shot will have less killing potential than say size 4 shot both will kill at close range and at close range there are more balls with 8 shot. Basically a 12 bore cartridge hold a 1/12 of a pound of lead, so the s