My Mossberg 500 has the straight conventional stock. I concur with FirstFreedom; if you're gonne mix it up at close range, and reserve the right to use you longarm as a melee weapon, the conventional stock is superior. Mine has a bayonet, so even doubly so.
My Benelli has a stock and pistol grip. Along with rifle sights, it seems to be a more natural, pure shooting configuration for more distance work.
Got a Winchester Defender with only pistol grip. This was for its compactness; first it was my one of my truck guns, now its one of the most destructive things I can shoehorn into my 350Z
Shooting this is definitely an acquired taste. I put on a pistol grip forearm, which helps marginally in taming recoil, but most of it still comes straight back into your shooting hand.
Pistol grip shotguns are absolutely not for everyone, and take some getting use to.