Significantly.
I don't really get many enthusiasts in Home Defense Shotgun. It's primarily normal people who are looking for some information on home defense and some skill with a firearm that will allow them to capably defend themselves should the need arise. Those fractions of an inch make a significant impact on where, exactly, they can mount the gun. The more inboard they can get the gun the better they can manage recoil. Recoil management is the key to allowing someone to actually train with the weapon to the point of competence or proficiency.
The enthusiast who will work with the gun even if it is sub-optimal is going to find a way to cope. It's actually the non-enthusiast who needs a shorter stock the most.