Somewhere in this thread it was mentioned 12 & 20-s do as well as the 16. Agree on the 12. DO NOT agree on the 20. A 20 ga is pattern challenged no matter what you put in it.
That said, as far as breaking clays or killing game birds... putting the bird in the pattern supplants anything else for effectiveness. The effete little 410 is more deadly than a 3 1/2" 12 if you aren't on target with the 12 & are on with the 410.
BTW I have about a dozen 16-s, mod 31, mod 1897, mod 59 remmy, sportsman 48 remmy, belgian guild gun sxs, marlin 90, 3 mod 37 ith. & some strays around here...

"Carries like a 20, hits like a 12" works for me.