With ARs, the advantage isn't just the lower recoil, but it's the options and enhancements that are available. From low-mass bolt carrier groups and lighter springs to drop-in triggers, a wider array of brakes/comps, and different forends for how you like the feel of your rifle. However, with where you're at right now, you're perfectly fine with everything you have.
With shotguns, the 870 will do well for a while, as there are a lot of mods you can buy for it. If you decide to upgrade to an autoloader, many companies offer a competition gun that will work for 3-Gun. Honestly, 3-Gun has probably been a saving grace for the tactical shotgun industry since the AR15 has skyrocketed in popularity.
I'm a big Benelli fan, and a strong believer in the inertia recoil system. I own two Benellis myself, and both have been 100% reliable for thousands of rounds.
The Benelli Performance Shop M2 3-Gun
is a great option for when you want a serious upgrade.
Another option that has gotten a lot of attention lately is the FN SLP MK1
. It's a gas operated system.
Otherwise, any competition trap/clays shotgun, or any tactical grade shotgun will work.
Benelli M2, M4, SuperSport
Remington VersaMax Tactical, 1100 TAC-4
The other option is the Saiga 12ga shotgun, which is fed by box magazine. This is also a very popular option due to much faster reload times.