For turkey hunting, some people made the switch to a 20 gauge, but me personally, I would never shoot anything except a 12 gauge, and a 3" gun specifically. It's all about getting the maximum payload to your target. Some say it's the weight thing, but really, how much does a 12 gauge pump gun weigh? For what it's costing to try to "soup" up a 20, might as well stick with what works, as in a 12 gauge.
Now about youngsters just getting into hunting, a 20 gauge might fit them better recoil wise than a 12 gauge.