Throwing hunting into the mix, I typically run Modified when I'm using Hevishot on ducks or geese. For pheasants, I almost always use Full. When I'm going after grouse or woodcock, then it's Cylinder. I've only shot doves a couple of seasons and still don't know if I prefer open or tight chokes.
BTW, about two months ago, I started experimenting with shooting sporting clays using Skeet... even for pretty long targets. So far, I'm impressed with how far out the clays will break cleanly.
When I start shooting tournaments again this year, I'm going to try underchoking from how I shot last year and see how it goes. For sporting clays, I've pretty well settled on carrying a pair of Skeet, a pair of Light Mods and a pair of Heavy Mods. Last year, I used the Skeet only for the closest of shots, with the Light Mod for mid-range and Heavy Mod for the long stuff. Now, I'm planning on Skeet for the close and mid-range stuff, Light Mod for the longer stuff and save the Heavy Mod for truly long-range (or long shots on minis and midis).
I still like to practice with tight chokes, though. I think they help me be a bit more precise and it's easier to "read the breaks".