There are people who can shoot pump shotguns as fast as a semi-auto, so technically you could use either. You'll mostly see over-unders on a sporting clays range, but according to the articles I read in various places (and my coach) semi-auto's are the favorite among the pro shooters.
In my case, I use a Berreta 391 Eureka sc in 12ga. I don't know how much difference there is among the pump guns, but the 391 is tops among semi-auto IMHO because it will shoot anything from light to heavy without changing anything. Recoil isn't even noticable to me, but this is highly subjective.
For the peson wondering about the 870 Trap gun:
I have the original model and LOVE it! The recoil reducer lets you shoot the gun all day long, and it's deadly accurate. It had been out of production awhile, and this is some sort of anniversary model I hear. If you want a gun JUST for trap, go for it!
DE137: Try shooting like this: Hold the stock against your hip international style, and only shoulder the gun when the bird is in the air. Make it harder still by having someone else do a slow count to some number before you can bring up the gun. Shows you if you're mounting the gun right real quick
