Personally, if my shotgun had a pistol grip and I didn't have a pistol, I'd sell the shotgun and buy a handgun!!
In all seriousness, I personally believe in a backup. I've read lots of opinions that you are better off carrying an equivalent weight of ammo & magazines than you are carrying a handgun. They are entitled to their opinion, but I don't agree. The nature of the world is such that the unexpected, unintended, and undesired happens at the most inconvenient time. Just a month ago I was at a gunshow where one exhibitor had several rifles that had been struck by enemy gunfire. The chance of a round disabling my rifle, running dry at the wrong time, etc. has convinced me that if possible, I would always carry a handgun as my secondary weapon.
The pistol gripped shotgun however has too much against it. It is too heavy, cumbersome, slow to reload and inaccurate to carry as a backup. If you could hit someone with it, great, but my handguns have 3-4 times the effective range at least, can be fired faster, hold more ammo and can be reloaded faster.
The pistol gripped shotgun has been glamorized by Hollywood, but has minimal practical value. Not a flame on you, just the gun.
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Dorsai
Personal weapons are what raised mankind out of the mud, and the rifle is the queen of personal
weapons. The possession of a good rifle, as well as the skill to use it well, truly makes a man the
monarch of all he surveys.
-- Jeff Cooper, The Art of the Rifle