Longer barrels swing more smoothly and are considered better for predictable targets. Shorter barrels are both easier to maneuver in restricted spaces and are quicker to point. They are considered better for combat or unpredictable birds. Longer barrels give you a longer distance from the end of the barrel to your eye, making eye alignment less critical. This makes them more accurate.
There is a slight increase in muzzle velocity with longer barrels, but it's not enough to worry about. More important is the increased flash and noise when shooting a shotgun with a short barrel.
I myself can't see the need for a short barrel shotgun after owning one myself.
I'll stick with the slightly better patterns I get with my longer barrels where I can see the difference on paper or game.