I've seen plenty of ducks and geese fall to the 20 ga. I don't use one myself b/c I just don't have the right gun for it, but as the others have stated, if the bird is in range there's little reason to think a 20 will not be effectively lethal. Sure, pellet count may be less than in 12 ga., but same materials moving at the same speed do the same job when shot well. I personally use a 12 ga with 3/4 #5 1.25 oz. lead for turkey in an old tightly choked Ansley H. Fox for turkey. I'm not a world class caller, but insist on the bird being in close b/c that's what makes it fun. If I can't get the old boy in I let him do his thing and try again another day. If I had a 20 ga. choked down tight and new it shot a dense pattern, I don't think I'd hesitate to take it in the turkey woods. Just my 2 cents.
Best,
jmc