Previously stated about 16 gauge -
It's lighter then a twelve (not always), bigger punch then a twenty (nonsense again, look at all the 3 inch 20 gauge loads). It carries, shoulders, and swings better then both (only in a better proportioned 16 gauge gun than the 20 was).
16 gauge guns are interesting, partly because they are different and scarcer than 20 gauge guns these days. You might even say they are a fashion statement, for the person who wants to stand out from the crowd.
There is no special magic in the diameter of the pipe, though the square load proponents might disagree. The 16 gauge inevitably became obsolete when clay target games focused on 12, 20, 28 and .410 shotguns. The manufacturers of guns and cartridges put all their modern developmental energy into the 20 gauge for upland hunting guns.
Certainly recoil is in proportion to the weight of the shot, powder charge, velocity and weight of the gun. There is no free lunch.
Having said all that, I have a 16 gauge AyA that I am quite fond of.