For the most part, a full stock is the better choice. But there are a few circumstances where I prefer a PGO shotgun. But NOT with the typical pistol grip which is angled much as a true pistol grip would be angled. That's a bad angle for the wrist to work a shotgun, especially as the gun is moved lower from line of sight.
The best pistol grip I know of is the Speedfeed "Birdshead" grip which is shaped just like the shape of the neck on a standard butt stock... not down toward the ground, but back at a gentle angle. You hold this just as you would a regular full stock, but there's no stock extension back behind your wrist. Imagine a regular shotgun stock with the back cut off just behind the "neck".... that's the shape of a birdshead grip.
Shooting from the hip may look rambo, but it's about the worst choice for hitting well. With the Speedfeed and the gun held at high chest level, about four or five inches below your line of sight it is possible to shoot quite well and quite comfortably.
For those times when you must have a really short shotgun, this is the approach which I would recommend. I have one shotgun (Winchester 1300 Defender w/18.5" barrel and 8-shot capacity) permanently set-up with the Speedfeed Birdshead grip and it's a real nice short shotgun to have handy, along with my full-stocked shotguns.