10 ga
I've only a bit of experience with the 10 ga, a brief affair with customized Browning BPS set up as a turkey gun. And it is true that on paper, a 3.5" 12ga is the equal of the 10 payload wise.
I'm no so sure that is the end of it though. Alloy framed 3.5"/12's will kick you silly. Built on the 12 gauge frame, but launching the heavier payloads, they get your undivided attention. A gas gun semi helps, but many of the 3.5/12's are affordable pumps. And they will bite you.
I think we may have reached the limit of reasonable shot column when the 12 ga went to 3 inches. At 3.5", a lot of shot is exposed to deformation thru the 12 ga bore. Modern space shot and wads, and overbored 12's may likely have solved this problem, but at considerable cost.
With lead shot, the bore of a 10 gauge, unless the 12 has been overbored, offers more room, and the shot cup more space, and theoretically should give more uniform patterns with the same payload.
The custom BPS was grim death on gobblers with common lead #4 shot, to distances farther than I'd ever consider shooting a 3" 12ga. And it was built on a steel frame that seemed bigger than a 12, which made it heavier and softened recoil, or so it seemed. But it was just too dang heavy to hump from ridge to ridge chasing gobbles, and I did not keep it long.