Apples and oranges. Hand grenades will take geese, too.
The 20 CAN take a goose reliably up close if they're inside 30 yards. But, if it's one of those blue bird days and they ain't comin' in closer than 50, might as well go home. Steel shot rules mean you can't use big lead and a 20 I'm unsure if you can even get 20 gauge 3" in BB steel, probably, would have to look for it. Maybe number 2 steel, it would work to 30 yards. But steel shot loses its umph fast past 35 yards even in BB steel from a 3" 12 which would pattern a lot better than 20 gauge. 20 gauge doesn't hold a lot of big shot and the patterns will be mighty thin.
There's more to goose hunting than backing off 30 yards from a tethered goose and shooting it.
And, yeah, a rifle, even a .22 short, will take a goose down, it's basically a lead bullet the diameter of a Number 3 buckshot and packing a LOT more energy than a steel BB and maintaining good energy to 100 yards. Shotguns are not rifles and wing shooting is not rifle shooting.
You do enough goose hunting with a 20, you'll wanna move up, trust me. If 8 gauge was legal and I could get one with ammo, I'd be using an 8 gauge. I wouldn't need it on a good day when they're decoying well, but it'd sure be handy at those longer range shots with Ts. Even the ten gauge's pattern runs thin past 60 yards, but really, that's all I ask. If I can't get 'em down to 50 yards are so, that morning just ain't meant to be. Now, if I'm pass shooting like I did when I was a kid, longer range is the rule, but over deeks, generally, you can get 'em in under 60 yards even on a blue bird day if they're at all interested, even in late season. But, they'll be very wary to come in much closer on many mornings.
You get on out there and shoot some snows with the 20 and get back to me. And, btw, shooting geese with a rifle is illegal here, and I'm thinkin' that's a federal law. If I saw anyone doing that, I'd call the operation game thief 800 number.