RE: 20 or 12 guage?
The only real advantage you are going to gain with a 12 ga would be with turkey. You will be able to get a larger payload and possibly some extra distance with a 12. However the recoil of these loads is pretty severe. A 20 ga with some good fast pheasant loads and a full choke should work well on turkey. They make turkey loads for a 20 ga as well. And if you are using a rifled barrel for deer and modern sabot loads they work excellent on deer.
Paul