the patterns are the same at the various distances with shot just a little denser pattern with the 12 because of the higher pellet count...
I agree with everything you said BUT, you left out one important bit of information.
On pass shots, the smaller guages have a "longer shot strings", so the duck flyes through LESS shot and that means less shot hitting the bird. That can and does make a difference on longer shots, but that doesn't mean i don't like 16's and 20 guages!! I have two drillings in 16 guage, and also other shotguns in 12, 16 and 20 guage.
My father always shot a Rem. 16 guage semiauto, and he killed ducks and phesants like i've never seen anyone else do!!!! I've seen him make so many tripples on game is isn't even funny, and one time we flushed a "bunch" of roosters (pheasants) and before they got out of range he droped 4 of them!!
Anyway, my father will be 92 next month, and although he gave me his 16 auto, he still uses it on pest around the farm to this day!!
Drilling Man