I have only killed a couple of turkeys, both with 2 3/4" 12ga, but I fully believe either could have been killed with a 20ga with proper loads. I killed one blue goose with a 3" 20ga using 1¼oz #4s (lead) in a Federal factory load. (close to 40 yrs ago). I recall "Reading" (not actual personally known to me facts) also many yrs ago, pre lead ban, about a Texas Game Warden who regularlly goose hunted with a standard 20ga shooting #7½s & used decoys & called in his geese & never shot beyond 35yds & held forward enough to insure hitting in the head & neck.

Miller/TN
I Didn't Say Everything I Said, Yogi Berra