here's my 2 cents !
i have shoot consistantly better on walk-through sporting clays courses with my 20 gauge O/U browning witha 32" barrel than with my 28" O/U browning, same gun, same chokes, different barrels, at least a 5 bird difference. who knows ??!!???
when shooting over dogs, i use the shortest barrels and cylinder chokes or most open choke available. a fast mount is good and the shorter barrels are lighter and are a little bit, not much, but just a little bit faster on the mount.
short barrels are also a minor advantage in the thicket, once again not much of an advantage but when you are chasing a ruffed grouse with the bead in a thicket you need every advantage you can get.
for trap i use a 34" shoulder mounted cannon :-D it seems to shoot better than any gun i've tried. for skeet i use a 28" 20 gauge O/U with skeet chokes, and a 410 SxS with full/full chokes.
can't offer you much on goose or duck hunting, havent tried them yet.
over the years, i have figured that if you are on target and got your lead straight, the barrel length and choke minor variables. if you like the gun and got your leads down pat, not much else really matters.
sg