Some considerations regarding the 20 v 12 question.
Yes for deer hunting, given a good & proper shot to the vitals, either will cleanly dispatch a deer.
However there is no guarantee of perfection. Sometimes a shot goes a little low, a little high, a little forward or a little back. And that is where it may be good to consider the answer to this.
If you were to be "run thru" in an area of your body, not directly thru a vital, but maybe pretty close, would you rather have it be with a .615" (20 gauge) round shank or a .729" (12 gauge) round shank?