The 20 ga. will do. As mentioned before, the primary difference between the 20 ga. and 12 ga. as far as killing gobblers, is that there will be less shot at any given distance all else equal. The momentum per each BB is about the same. I would "guestimate" that 25-30 yards would be a dead bird. But you need to pattern the gun and load. If I were you I'd use a "turkey" target. If you can get roughly 10 pellets in the head/neck region, its a dead bird and that is about the effective range. My daughter uses a 20 ga., 3" with a Rhino turkey choke. Does fine about to 35-40 yards using Winchester Supreme #5's.