With the ammo that they are putting out now I don't think that a 20ga lacks anything except pellet count to a 12ga.
Though I haven't taken any large Westerns with the 20 I have slammed some Lessers with #6 Heavyshot at pretty crazy distances as follow up shots for others. I never shoot #4 or #2 so I can not say there. If you want to shoot cheap basic steel loads 12g is probably going to be a better fit for most waterfowl. But get into the premium steel alternatives or have upland birds on the menu I give the edge to the 20g. I also find the factory chokes for the 20 pattern better than most factory 12g chokes.
If I ever found a need to sky bust westerns I'd probably want an aftermarket choked 12g or even a 10g. But, I most certainly don't want to be lugging that thing around the good chuckar grounds. And when it comes to pheasant and quail we pick enough pellets out of them shooting the 20's. When I shot 12g for pheasant and quail we made a lot of bird burger and sausage because they were just blown to heck. Although part of that is having good dogs too. Sometimes you just can't hold back the excitement for the count of four before making smoke

I find most folks that bad mouth the 20's either hate eating wild birds or have never actually shot birds with the 20.