Recoil is recoil. KE is KE.
TL3 = Blunderbuss
TL4 = Double Barrel Coach Gun
TL5 = Pump Action Trench Gun
TODAY = Semi-Auto Shougun / Full-Auto Shotgun
Ammo has made some improvements and Actions (loading) has made significant improvement, but MARINES have employed roughly the same Ammo at roughly the same KE for hundreds of years because it does the job well.
Ammunition is where almost all of the significant changes have happened with smoothbores.
Going from loose powder, wad, and ball to self-contained cartridges
Different loads giving better lethality--from slugs to variable ball size and number
Specialized ammunition types like:
Case--originally cut shells, but now a sort of shrapnel round that goes out as a slug and then breaks open scattering shot at the target end.
Flammable--like "Dragon's Breath" using flammable metals ignited on firing
HE--in various forms turning the shotgun / smoothbore into a grenade launcher or small anti-armor weapon.
I could see guided and other 'intelligent' rounds being developed in the future for use with these weapons. By something like TL10 to 11 I'd say they could be launchers for tiny, guided missiles. I could envision something like that for even a bow or crossbow.
It wouldn't be the weapon that would be controlled by law so much as the ammunition. So, you could have the shotgun, but you couldn't possess things like high explosive guided rounds for it, or ones where the shot was some sort of quick acting poison or whatever. That stuff could easily be illegal on a world where shotguns are otherwise allowed.