I own a number of both and shoot them, I think, equally well. For estate type quail hunting, I use either a Grulla .410 Sidelock SxS or a William Atkins 20 bore. For wild quail or huns it is usually the Atkins or a Luchini hammer 20 bore. It works well on quail because it is a modern built hammer gun with a normal safety. In other words, it works just like any other OU or SxS when cocked and on safe. For doves, I typically use a 20 bore OU "Inverness" by CSMC or a tightly choked 28 SxS by Darne. For pheasants, I have a number of SxS twelves that are most often packed for the trip. Competitive pigeon shooting is with guns built for that purpose in both SxS and OU configuration. My primary waterfowl gun is a CSMC 12 with 3" chambers - though I only use 1 1/4 ounce loads for ducks or geese - and never ever use steel. I might also add that I never use 1 1/4 loads on pheasants. A properly choked light game gun with 1 1/8 ounces of number 6 shot is perfection.
From a purely aesthetic point of view - nothing beats a SxS.