I have been giving this question a lot of thought. I have been shooting 4 to 8 rounds of skeet a week between hunting season. My guns are basically game guns: 5-14 CSMC 20 gauge fox, 6-4 BSS sidelock 20, 6-10 Webley & Scott 12, and a 7-3 Parker Repro Steel Shot special. I do almost exclusively use 3/4 ounce loads of less than 1200 fps. I also use the Repro and Browning the most since they are a little heavier. Actually the Repro is fairly well suited for skeet shooting I think.
I like my bird guns and hate to think I am using them up on recreational clays. But part of my logic of clay shooting is to become a better wing shot, so I like using my hunting guns.
I have formed friendships at the gun range so I want to keep going. I have thought about getting some heavier guns such as a Parker on a 2 frame or maybe Winchester 21 (hard to find with double triggers). I have even considered looking at OU such as Merkels or older Berettas with double triggers.
I would like to stay with side by sides, but the big question in my mind is will they hold up. May be buy more guns to put in the rotation, lessening the strain on each. I like that idea.