There can often be some confusion over these terms, but when you say pistol grip, do you mean just the pistol grip, or pistol grip with a buttstock?
PG only shotguns make me laugh. In all honesty they take the worst of everything and stick it together. I can see almost no purpose for a PG only shotgun, other than maybe if you were planning on having a gunfight in an elevator. You can no longer aim worth squat. Recoil is much more difficult to control. I just don’t see how they can manage to sell these, unless it is to those same guys who have laser sights, heat shields, and a bayonet on their PG Mossberg.
PG and a buttstock. These work fine. Just depends on what you are more comfortable with. Note, if you are an 870 shooter, some of the PGwB stocks will make it tough to disengage the safety easily. According to some people the PGwB has less felt recoil, because the recoil comes straight back. If this works for you more power to you.
Folders. Most suck. Some suck less than others. I haven’t used one that I like yet. The top folding Remington police model is designed to kick you painfully in the cheek. I believe it was designed by an antigunner in the hopes of teaching us to dislike shooting. (kind of a Pavlovian thing).