There sure are a lot of experts around here...
Just because you say something is fact doesn't make it so. Energy doesn't just "dissolve". It's simple physics. Yes, when you adrenaline is pumping it may be less noticable, but it doesn't change the sheer physics of the problem. More is more, even in the worst public schools. But I'm not sure that you get to determine when the difference is negligible, and this discussion is about the theory behind it and applying that theory to real life. More recoil, even in the slightest, increases your time to next shot, all other things being equal (reliability, trigger, weight, technique, etc).
They are not fundamentally different, and they surely aren't on opposite spectrums of weaponry. But please feel free to "educate" me instead of copping out with a statement like "any reasoning about recoil may be lost in an explanation". If fit, swing weight, "pointability", choke choice, ammo, technique, etc is all the same, can you really sit here and tell me that recoil has no effect? And are you REALLY going to sit here and tell me you get ZERO muzzle rise from your shotgun?
Yes, recoil has more of an impact at distance. Not sure anyone ever said otherwise. But I would argue that static clays at longer (shotgun) distances are just as challenging as any offhand rifle shot at distance. It's all relative. They are different enough that 10 yards on shotgun doesn't equal 10 yards on rifle, but then again the targets are different as well.
I think some people are interjecting other issues into the discussion. The title was "shotgun recoil", not "which shotgun has the best recoil compared to all other factors related to that particular gun and all other external factors not regarding recoil". And for the record, I shoot a Benelli.