My own personal preference is the pump shotgun, for several reasons, although I own every type of shotgun there is (except lever action). If one is in a hunting situation and has to cross a fence, it's easier to simply slide back the slide handle, pick up the ejected shell, cross the fence, then drop the shotshell in the barrel and (with the muzzle pointed in a safe direction, pump the handle forward to chamber the shell and keep hunting.
If you accidentally drop a shotgun in a creek, a pump is easier to clean out than a semi-auto. They're also usually lighter. Also, there are no recoil springs to maintain, no gas ports to clean, simple maintenance.
Semi-autos do seem to kick less and avail the shooter quicker follow ups, though. When I hunt with a semi-auto, I find that I'm more likely to waste ammunition. With a pump, I'm more likely to take my time and take better shots.
I've never really mastered the over/under....or the double. I guess I'm a pump guy. I like 870s and 500s and I think I shoot them better than anything else, all things considered.