It's been a while since I had direct access to the Fed database,but last time I looked,all gauges and loads had about a 98% overall stopping rate.
I doubt any perp will be able to tell if he was shot with a 12 ga or a 20, nor will he care.
Some LEs I know have gone to varied 20s for raid guns, doubles, pumps and autos.
My HD shotguns are 12 gauge, but if all I had was the 20 ga Youth Express I got for the kids with either the 21" Remchoked bbl or the 20" slug bbl, I'd still be effective and downright dangerous.
As for HD ammo for the 20, 7/8 oz of lead anything at typical HD ranges will be effective. I'd mix load,if t'were me, with a couple birdshot loads up first, then a pair of #3 buck.
One caveat:
Many 20 gauges are vicious kickers with most loads. The lighter weight of the 20 ga offsets the lighter load,and oft the butt of the 20 ga is smaller.