I've killed geese with my 10 ga (the one with intact barrels) and it does quite well. It's hell on a bunch of hogs at a feeder as well with buckshot.
I've probably used it more for killing cripples (ducks) than anything else. They will reach a bit farther than a 12 gage and put a lot more pellets on the water.
I don't think the short barreled one would kill a goose. I shot at a cardboard box yesterday at about 15 yards and the patter of those BBBs was out to about 18" (guesstimation).
The good thing about substandard metallurgy and 10 gages is that you really don't want to shoot them all that much.
I started with an Eastern Arms dogleg 410. Still have it. All my boys started shooting with it as well. In South Louisiana my dad wouldn't let me carry a 22 or buck shot when I was out in the swamps. I clandestinely cut the ends off paper shells, empty the shot, drop a 36 cal lead balls in the case, and fold the top over. It made kind of a "plunk" sound when fired and was reasonably accurate (reasonable for a 11 yr old kid making his own ammo). I had killed some rabbits and my mother had fried them. My dad remarked at the meal how they didn't have much shot in them. I allowed as to that they were probably just hit in the head.... about that time he "clunked" a slightly deformed lead ball (with a few teeth marks on it) onto his plate. He just said, "Yep, Probably". He never said anything else about it, and neither did I....
Alan