Can't add much other than personal experience. My handle is a clue to my preference, and the only 12 I own is limited to turkey and waterfowl. Otherwise, the three sxs 16's get the nod. I have a large build and very large hands, but a 12 just feels like a cinder block married to a 2x4. Likewise a 20 or 28 is too small and whippy, the recoil in the former sharp and wicked with many loads. The 16, to me, is just right. YMMV.
A short time ago, someone posted that if he needed to shoot 7/8 or 3/4, he just picked up a 20 or 28. I am not a natural or a great shot, so anything I can do to keep following the fundamentals is a plus. Thus it makes sense for me to change the load, and not the gun- perhaps not unlike subgauge tubes for serious skeet shooters.
You do have to be more proactive with your ammo than a 12 or 20, but it's not the big deal that skeptics claim. I reload on a PW 375c, and mostly load 65's since two outa the three are 2.5 " chambers. I'm loading them mostly with 3/4 oz, and if I do my part, am consistently surprised how far out they will break targets. This one load covers me for targets, quail, and dove: for roosters and grouse I have a flat of RST 1 oz mixed (they do so happily for you) between 6's and 7's. One oz is usually plenty: I took out a long, crossing rooster the last week of KS pheasant season this year with an ounce of RST Lite 6's in a 65mm hull out of a light mod barrel. Post-mortem revealed numerous pellet strikes going past the meat well into the vitals.
The 16 has been called Queen of the Uplands for good reason, and is my go to gauge for even more. Long live the purple shell.
Mike