My experiences and not scientifically tested are, the best shooters down cleanly the most birds. Although there are game limits I want to try to kill cleanly and not leave cripples when ever possible, if a pattern is more efficient with less thin spots it should kill cleaner. Most 16 bore shotguns are lighter then 20's or about the same therefore I like 16's to carry lighter and mount quicker then most 20's (not all). If I am hunting late season wild pheasants, I prefer a more modern 12 that can handle a hotter load.
The most important aspect is to work on your shooting and you will kill more and more cleanly.

Jeff G.
I hunt mostly with 16's but also use 12's and 20's depending on game bird and wild or not. and also the type of dog and terrain can play a part. Mostly I pick the gun I shoot the best.