While I am far from an expert turkey hunter I have taken my share of birds. All were with a 12ga. using #4 shot. I would have to say that a 20 would likely be fine if you are not trying to reach out to far. That simply means you need to be more patient and a better caller to bring them in close enough for a clean kill with a 20. I'd guess that ducks and geese would be the same. You just need to shoot within the limits of the gun. But I'll stick to the 12.

Bill G.