Just off the top of my head without digging into ballistics info from what I have learned before I bought my 20 for bird hunting, just a few less pellets per load and as far as power it might only be lethal out to 40 yards instead of 50-55 with a 12.
Tacticly a box of 20 is a bit lighter than 12, smaller easier to handle.
A con may be that 12 is sort of the norm so in a SHTF situation 20 will be less prevalent.
ETA: Trench Coats look cool.