Budget is one issue....and there are some semi-autos over $2,000 .....like Benelli's primary clay target gun the Super Sport...listing at about $ 2,199..
http://www.benelliusa.com/supersport-shotgun
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But that isn't really the issue. All clay target games restrict you to no more than 2 shells..... 3 gun competition is a whole different deal.
Discussion of Point of Impact with a semi-auto vs an O/U....if the barrels on the O/U are made properly and installed properly - its called "regulated" ...then both the top and bottom barrel will have the same Point of Impact. Obviously its simpler with a one barrel gun like a semi-auto...but many O/U's hit the same spot ( not some of the cheaper O/U's made in Turkey, etc necessarily - but certainly most any Beretta or Browing will hit the same point of impact).
Cycling speed...semi-autos take time to cycle / some are quicker than others...but in general, an O/U can fire both barrels quicker than most semi-autos will cycle -- because the recoil on an inertia trigger O/U just resets the trigger and its quick .../ but we're splitting hairs here....they're both pretty fast - at least modern semi-autos are quick ( not so much the old Auto 5 technology )...
reloading speed.....isn't an issue in clay target games / you're restricted to no more than 2 shells max. ( there are a couple of odd 3 shells shoots )...but Trap, Skeet, Sporting Clays and 5 Stand all restrict to no more than 2 shells. 3 gun competition is a different thing...
Can you hunt with an O/U with 2 shells sure...can you eject the 2 spent shells and drop 2 more in, sure....is it practical, probably not. So maybe a semi-auto in terms of hunting has a slight edge / because most hunting laws restrict you to one shell in chamber and no more than 2 in magazine for 3 shells total.
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Top end "target grade O/U's" are Kolar, Krieghoff, Perazzi and Blaser...and they all start in the $ 10,000 price range and go way up from there....Beretta / Browning give you a lot of gun for the money in their upper level guns at around $ 3,000 - $4,000....with a lot of features. Brownigs entry level, field grade O/U's ....like the Lightning series...sell new for around $2,000 ....they're solid guns / have the same barrel to receiver connection as the Citori's do at $3,000 ...but not all the same features in terms of adjustability.
Adjustability is a big deal on a Shotgun ...so it hits where you look. If you have an angled comb shotgun ( on an O/U or semi-auto or pump ) ...then as you go from season to season ( shoot in T shirts in summer, heavy coats in winter...then the point your face sits on the comb moves up and back / and that causes your muzzle to move up and down....so your Point of Impact changes .....so many target guns / and hunting guns...shooters want a parallel comb gun ( where comb is parallel to rib )....so point of impact is the same winter - summer - hunting - etc....
I have no issue using the same O/U ...Citori XS Skeet model with 30" barrels in a 12ga at about 8 1/2 lbs....for waterfowl, upland birds and most all the clay target games....one gun, that does a lot of things.
But getting started ....is a Citori Lightning your best choice ( I would say no ) even though it is a gun that you will pass down to your family for 3 or more generations.../its not your best clays gun.
For Trap specifically ....there is less left to right barrel movement than the other clay target games...so most of us that Shoot Trap will have a dedicated Trap gun...that is longer and heavier than our general use guns...for Trap, I go to a Citori XT Trap, 32" barrels, 12ga and around 10lbs...the heavier weight helps with the follow thru.
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Shotgunning ....whether its clays or live birds...is a pastime where "follow thru" really counts...pulling the trigger is the start of the shot, not the end of the shot....the end of the shot, is keeping your eye on the target and following thru. The lighter the shotgun - the more "whippy" it feels...but its a personal thing....at 6'5" and 290 lbs what feels "whippy" to me - and what feels "whippy" to my buddy at 5'10" and 165 lbs are 2 very different things...so its personal. But in general, if I go to a light gun ....like the Benelli Super Sport ( 7.2 lbs ) for a general purpose gun, I go with a longer barrel, so in that gun, I go with a 30" barrel on the semi-auto ...so the longer sight plane helps me smooth out the swing....vs "swatting" at a target... 30" barrel in a semi-auto and a 32" barrel on an O/U are about the same "overall length"...
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But a good semi-auto or even a pump gun ....with a 28" barrel and changeable screw in chokes...is a good all around gun / good starter gun.
Citori Lightning is a good starter gun...
Many of them have angled comb stocks...so you might have to put a comb pad on them / some of the semi-autos come with shims between stock and the receiver ...so you can change the angle of the comb...many don't .../sometimes, that's part of the cost as well...
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O/U's ....where you have 2 barrels.....and you can screw in different chokes in the upper vs the lower barrel....make that gun more versatile. If I shoot a semi-auto ....I have to pick a compromise choke. If the target setter on a sporting course....has a long crosser out to 40 yds ...going fast and dropping downhill ( I may want a Mod or Imp Mod for that target )...and the 2nd target floats in overhead, sliding and falling across my shooting area, I might only need a Skeet choke for that one.../ in an O/U no problem, I set one barrel ImpMod and one Skeet....if I shoot the semi-auto ....I have to go with Imp Mod.../ and might only have an 8" pattern at the close bird ( not my best option, if my score matters in a tournament).....but if I'm just shooting for fun with my buddies, who cares....