A coupla things. concerning 20 gas, recoil and fit....
First, only big payload missions like geese and turkey hunting shows a clear advantage to the 12 ga, as long as ranges are sane. I've used various 20s on critters from squirrels to whitetails with perfect performance as long as I took shots of moderate range.BTW, the 20 ga Rottweil Brenneke may be one of the best deer rounds for close work there is. Blood trails with it run shorter than most 12 ga sabots leave.
Also, even classics like the Parkers can be a little heavy for upland game in 12 ga. A 20 ga double is almost guaranteed to be a great quail gun, assuming stock fit.
Second, the 870 Youth Express 20 ga here weighs close to 7 lbs, but still is a vicious kicker with 3" mag loads, or even some high brass 1 oz loads.Stock fit is more the culprit than Ft/lbs of pure recoil.
And on that note....
Fit and form are inextricably connected. Someone with great form can shoot OK with a poorly fit stock, a dud with lousy form can miss 25/25 with the best fitting stock in the known Universe.
But, most of us are shooting less than perfect fitting stocks, and our shooting proves it. A little testing and temporary modification can work wonders.
A note on the 20's kick. Since most 20s are physically smaller than the 12s, the butt is smaller also. The less area of contact, the harder the kick. Adding a larger pad will tame the beast a bit, but it might look a bit funny.
Finally, Pop used the same 12 ga Savage O/U for decades, until some lowlife stole it at a field trial in the late 60s. Friends bought and gave him an SKB 20 ga, choked IC/M.
He loved that little SKB,and shot it just as well as his old favorite...