Friends of mine who have used various rifles and shotguns tell me that there is only a small difference in recoil (note, I have fired both rifles and shotguns, just not enough to come to a proper conclusion by my own account). Shotguns are "in general" a little stronger when it comes to that, but it's nothing that matters much. I've used shotguns myself, and I don't feel the recoil is all that bad. The only time I really felt the recoil was when I used a very small shotgun with low weight. That hurt like a bitch - but only because it was the first shotgun I used, and I didn't close the gap between my shoulder and the buttstock of the shotgun.
In my country, most normal people have both a shotgun and a rifle. I've asked around, and no one claims shotguns have "far worse recoil". I question whether you have ever fired a shotgun at all - not to mention a rifle.
It also GREATLY depends on the calibre of bullet, or what gauge of shotgun shell you're using. But I guess you didn't look too much into that. And obviously a burst fire from a rifle would be felt fairly well (again, depending on ammunition type).
The Norwegian military's former assault rifle was 7.62 calibre, and friends of mine who have been in the military say it packs more of a punch than any shotgun they've used.
Usually the term "rifled shotgun" applies to a shotgun used to fire slugs, as they require ballistic efficiency to be of any use - so they exist, though one might question the definitions of shotguns and rifles in this particular.
Personally I find a shotgun to be much easier to use at relatively close range than a rifle. A rifle requires a precise shot and a steady hand, whereas a shotgun knocks most people down within 40 metres, and you don't even have to hit them dead on. Hell, the most efficient close combat weapon ever is probably the USAS-12 or its successors. No recoil, fully automatic. Kills anything you aim it at.
Anyway, like I said, why can't intelligence decide how well you can "link" the weapons together? Maybe it could decide the cap? Half of intelligence could be the cap of which one weapon "synergizes" with others which have some similarities.