Personally, I chose not to go with a semi-auto... Most of my shooting is clay shooting when I'm fortunate to have some time... and I shoot cheap trap loads. Owners of semi-auto's warned me that semi-auto shotguns tend not to shoot cheaper shotgun loads well at all. They explained that the cheaper metal at the base of the shell and plastic shell itself both expand more in cheap loads, which tend to cause semi-auto shotguns to jam. Thus, a semi-auto was not for me.
I would have to wonder what autoloaders they were talking about.
I have a Browning B2000 (which I would be happy to argue is the nicest looking semiauto shotgun ever built) and my brother has an old pogo stick (i.e. Browning Auto 5). We got those back in the early 70's, and believe me, with what we made back then we bought the cheapest 12 gauge loads we could find before we got smart enough to buy a PW and start reloading.
I've never had problems with reliably feeding anything in my B2000 - and I often used the 3" barrel in that gun instead of the 2 3/4", because it was modified while the non-magnum was full. My brother has never had any problems either with the 'ol humpback. In fact, he's mumbling about buying one of Browning's new versions that will be compatible with steel shot.
Those two old autoloaders have nowhere near the technology built into them as the autoloaders of today, I'm pretty certain of that. The autoloaders of today are way more advanced than ours. So it is hard for me to believe that autoloaders have suddenly become unreliable, on or off the trap and skeet fields.
It is a pretty valid concern that auto's throw your empties on the ground, and at many clubs, what hits the ground belongs to the club. The partial answer to that is a shell catcher, which I used on my B2000. Didn't help with doubles and skeet, of course...
Speaking only for myself, I would put most of my attention into finding a shotgun that fit me well, rather than agonizing over the differences between operation. And how much I liked the feel of the gun as you mounted and swung on a target. That's what's going to make the difference in your hits versus misses, not whether you have to cycle it by hand or it cycles itself.
And then of course, there's the issue of looks. Life is simply far too short for ugly shotguns. My life, anyways. And so I've become a victim of the urge to own and shoot classy looking (to me) over and unders and old side by sides. My B2000 gets a bit of use and it really does soak up recoil - but there isn't much recoil with even the heaviest of pheasant loads anyways. Dad's old Model 12 gets almost no use as pumps just don't stir my heart strings. But the old N.R. Davis side by side that's close to a hundred years old and the new Citori Satin Lightening that's arriving any day... now those kinds of guns get my attention.
The OP knows what appeals to him better than me or anyone else. I'd go to the local trap/skeet/sporting club as earlier suggested, see if people will let me try the models I'm interested, and then choose the one which whispered in my head "Buy me..."