Pick one for the paperwork. Anything requiring brain cell activity will only confuse the examiner.
Now you may be dealing with 2 different classes of weapon. I think a pistol grip SBS is considered an AOW (any other weapon) or something.... and the stocked gun would be an SBS.
But since it's not a factory AOW, you're just going to be looking at an SBS.
You might run this by the NFA section on M4carbine.