Is there a big difference in recoil between the 12 and 20 gauge shockwave?
You will not notice it. Because in 20 gauge the firearm is a tad lighter. Now grant it if you go slug festing at the range in a 12 gauge you'll get a jolt. But these firearms are defensive tools first and foremost. You can blast all day at the range but be aware of your expectations. And being they are aluminum receivers they will not handle recoil better than Remington's Tac-14 with their metal billet receivers. Not trying to start war here, it's how that rolls.
As the others have made note and it works with that argument about setting a high powered gun off in the house without hearing protection or muzzle flash outside at night messing with your vision, which means none of that crap matters when the adrenaline kicks in. Adrenaline protects the senses.
But back to your concern, people who will have problems shooting these little blasters will be those who have own shotguns before.
You cannot shoot these things like a shotgun.
It's all about 'technique'.
I've notice in my research many are just buying these like a fad or something, then tricking it all out and will probably never make the effort to learn the technique. Which is not an easy thing to do if you don't have place to do it at. You can find a range who will let you shoot a rifle easier than letting you shoot shotguns unless you belong to a private club.
You have to pattern shotguns so you know what it will do with certain loads. I myself belong to a private gun club and we have to pattern on the rifle range at the 50 yard line and then move over to the shotgun range if we just want to blast around. If I didn't have those options I would never even consider getting one.
I'm on the fence myself.
I will say these firearms are some of the best tools in defense to come down the pike in decades. And all without dancing to a paperwork jig.
And I do feel encourage when I see video's like the one below that maybe, just maybe I could handle these little blasters. Take a look at it to get the proper technique down.
Good luck to you.