I got to play with a 20 gauge coach gun (again, I did not make a note about make and model. Yes, I am that absent minded) and I am going to say that I would not want to stand in front of that thing when it goes off.
This is two loads of buckshot. One is Aguila #2 buckshot and the other is Winchester Defender #3 copper-plated buckshot. In my uneducated opinion, they both performed nicely in the gel.
And this is Winchester 20 gauge 3/4 oz. slug after recovered from the gel. I did not take a photo while in the gel, but it went easily to the middle of the field of buck seen above and as you can see, expanded nicely.
The coach gun was a light one and even so, the perceived recoil was distinctively less that with a 12 gauge pump. I may have shot 20 rounds of both types and yes, I have a bit of soreness, but it is about the same if I had slept with the arm the wrong way or any other of the aches I have related to getting old.
I would say anybody who is recoil sensitive with a 12 gauge, would want to consider “downgrade” to a 20 gauge without feeling to have compromised performance.
I inherited my fathers 20 ga Mossberg Defender. The one thing I discovered was that there were a limited number of defense rounds back then. I haven't looked lately it might have improved.
Push-pull hold with a 12 gauge makes a considerable difference in felt recoil too.