The thing is, you shoot turkeys right in the head & neck with them standing on the ground with thier wings folded. Not flying with the soft underbody exposed like geese.
If you can get the 20ga. to pattern any smaller shot (say #5, #6, or #7 1/2) tight enough to put several pellets in the head & neck area, it will kill them just as dead as a 12 ga.
rc