A smaller bore shotgun will never be ballisticly superior to a larger bore. You can push it to get real close but it never catches up. Light weight guns are great with light weight charges but can turn unpleasant with heavy ones.
From a personal choice I'd pick the 12 with 2 1/2" chambers or even 2 3/4" chambers. More shell flexibility and easier for me to reload. But if you like the 20 or 16 more just use it and be happy. You can do just about the same with all three if you limit your range and adjust your shells to match your game. Plus you will find many times more 12's than 16 or 20's to choose from.
