the .410
My Dad and I hunted rabbits with the .410. We were serious rabbbit hunters mind you, and we had a pair of good beagles, half brothers, that worked together in a manner hard to believe. Dad once turned down good money, on the spot for those two dogs. I was never able to turn out their equal, likely my fault and not the dogs, but Dad's dogs, Jake and Jack, were fine.
We killed a truck load of rabbits over that pair, and did nearly all of it with .410 pumps choked full. The load was 3" shell....#7-1/2 shot. It was our experience at the time that shot any larger did not create a dense enough pattern. We never fooled with the shorter 2-1/2 inch shell. Ranges were short, thick cover often, and I doubt we shot much over 25 yds ever, sometimes half that. All that to say that the .410 can be a useful squirrel/rabbit gun when ranges are short.
On birds, the small thin pattern works against you. The .410 is not really a pheasant gun, those critters can be tough. I don't think it throws a useful enough pattern for grouse, and I'd likely never kill any doves with it, as I'm not a good enough wing shot. I think the .410 might work well for game farm quail, woodcock too, but I've never done any of that. But ranges seem short and the shooting in the open from what I've seen on the tube.
I've used the .410 to start kidsbeginners on hand tossed clay birds (like a frisbee), but for real clay birds, its an experts gun. Shells are expensive,and sometimes hard to find. When I do, their often the stubby short ones with a thimble full of shot. Anything a .410 can do, the 20 ga can do better, and then some.
All that said, I still own two, an old Win 37, and a Rem 870 Express. The vintage single barrel stands ready at the back door for reptile extermination,and sees some use every summer. The 870 has seen very little use, as I've gotten away from beagles/rabbits, but it reminds me of times gone by and there's hope I might get a good dog and a decent place to hunt bunnies again.
