Ok, so having gotten every Shotgun level 30+, trying Range and Damage on each, also getting gold on the USAS, SPAS, Striker and the Model 1887 I can say (IMO) that:
Best - Pre-patch, it was the Striker. But now, I have to say the USAS12, the range and damage is pretty good without anything on it, and Damage + Ext. Mags makes it a beast up close and pretty good out to a good range to.
Worst - IMO, its the AA12, yes its got a good fire rate and kill pretty quickly up close, but the range on it sucks. Even with Ext. Mags and Damage/Range its not the best. You could argue that the Model 1887 is the worst, but its actually pretty good once you get Damage on it. Also, the SPAS isn't the best at first, but when you also put Damage and Ext. Mags, its also a really good gun.
There you go, just what I think.