is the .410 severely under powered compared to the 12gauge, is 223 or 556 as powerful out of a shorter barrel, can upper and lowers be exchanged between AR rifles and Pistols legally without paper work, and is it as accurate without the stock or with an arm brace?
yes, less powerful than a 12ga, although "severely underpowered depend entirely on your frame of reference
yes, the .223 out of a short barrel is as powerful as the .410
Yes, and no. AR Uppers and lowers can only be swapped in certain combinations and be legal. Other combinations are not legal without prior Federal approval.
as accurate as what? Mechanically, the AR pistol matches the rifle. Practically, the ability of the shooter to BE as accurate with the pistol is extremely difficult. Of course, at across the room, it hardly matters...
I do find it interesting how so many people disdain the .410 slug, as being inadequate, and yet are fine with a 9mm Luger pistol...(which, even loaded +P+ is significantly LESS powerful)
the .410 slug, while not terribly heavy at 1/5oz (about 96gr) IS .41 caliber, and is moving out of a full length barrel at about 1800fps generating 700ft/lbs of energy.
Also interesting, a 55gr .223 bullet out of a 10" pistol barrel ALSO generates around 700 ft/lbs of energy.
Also, please note that "lesser overpenetration" of the .223 round applies ONLY when using soft point/hollow point "varmint" type bullets! Use ball ammo and the penetration is much greater, enough to nullify the argument.
as a back up HD gun, advantage to the shotgun, as you will be able to shoot it more accurately (it has a stock).
Advantage to the AR, magazine capacity.
Blast and flash, advantage to the shotgun.
Looking "evil" in court, advantage to the AR pistol!
Choose which ever you want for all the OTHER things you will use it for. Either will serve as an emergency back up HD gun. Neither is the best choice for either primary or backup, but they will serve if needed.