20 gauges work fine. Just makes sure you operate within the gun and load's limitations.

My youngest son killed his first turkey with an old Browning auto5 20 gauge with 2 3/4" number 6s and a 28" full choke barrell, at 27 yds, stone dead.

My oldest son killed his first turkey with a 20 gauge Nova using #5 HeviShot at 55 yds. (That was a case of misjudged distance and youthful impatience, but gives you an idea of what can be done with a 20 gauge.)

Hal