Great topic to start a spirited discussion!
If you already have a 12, I would personally go to 20. Which is what I have done actually.
My reasoning:
1. Practicality. 20 ammo is very easy to find in a wide variation of loadings and it is relatively inexpensive when these two factors are compared to 16, 28 or .410.
2. Evolution of ammunition technology has allowed both the 12 to "download" (if you will) and the 20 to "upload" to point that either the 12 or 20 with suitable loadings can easily fill in the old gap that the 16 filled between 12 and 20. The same can be said of downloading the 20 to cover the 28s habitat
3. A properly scaled and built 20 is a nice, light firearm in either Two or Single barrel configuration. Generally lighter than a 16s and very, very close to the 28s.
Those are essentially the reasons my gun safe has mostly 12s and 20s. The 20s are out in early season when shots are closer. When the wild flushes start, the 12s get the nod.
That said, I have shot (but do not own) some very well balanced 16s and 28s that patterned very well with the appropriate quail and pheasant loads. I hunted with a very good shot that used a 28 exclusively for pheasant and was deadly with it. He did not, of course, take 50 yard shots with it though.
As always, your mileage may vary!