There's no question, many shotguns are mainly plastic and can be quite light. Pistols "may" weigh more, but I can't imagine many do. The weight in a pistol either way is more dense and compact, but that means easier to manage and carry. A hip holster is out of the way and doesn't increase you profile. Also you can mount it anywhere so weight distribution isn't an issue. Pistols are easier to wield by leaps and bounds, no contest really. I'm certain a shotgun can be made quite accurate; air nozzle, piston, hop-up, barrel, seal, etc. But as a backup, I really don't see the benefit over anything. I'd almost consider carrying an SMG just for firepower and deal with the weight. I go from my primary to my pistol when I don't even need to, just because I want to close in my profile and react quicker, especially indoors or during CQB. To each their own.
ďREALITY IS LIKE A STONE. TO MANY ITíS HARD AND COLD, THEY CANíT HUG IT OR EAT IT, IT ONLY FRUSTERATES THEM AND DOESNíT DO THEM MUCH GOOD. TO OTHERS ITíS STRONG AND DEPENDABLE, YOU CAN BUILD WITH IT, BUILD UPON IT, OR WORK WITH IT, ALSO USE IT TO SMASH PEOPLE IN THE FACE.Ē