According to military repair shop records in WWII, the 31 required less service. Oh, also own a couple 37s in 16 and a 12 16ga.
Haven't hunted the 12 yet; not sure I want to. Might like it better than my 37s.
--When Vietnam reared its ugly self (Thanks LBJ) our USMC armories had both M12 and M97 12 gauge pumps in riot configuration- not many with the bayonet lug and heat shield that makes riot pumpgun collectors get all wet and sticky I guess. We also had some Ithaca M37 and some Browning-Stevens pumps- forget the model or nomenclature, but they were "humped back" like Browning's great A-5 autoloader.
Stateside base skeet was recreational plus there were some inner-service shoots, as there were for both pistol and rifle. We had mainly 12 gauge M12's with the Cutts Comp-- and also a big reloading set-up-- Enlisted personnel could shoot skeet with a box of 12 gauge reloads for $1.00 per round.
I used a friend's M31 12 gauge once- we were pheasant hunting, and I had one of my 12 gauge field M12's-- he had a good Lab and after we had each taken a rooster cleanly with out own shotty-guns, I asked to try his M31 (his father bought it new in the Depression years- 28" mod, solid rib- sweet handling indeed- but a big smart-#$% Rooster owes his life to the fact that the "go buttons" for the safety and action slide release are different from the M12's I grew up with. I had that big rising loud mouthed cousin to a peacock dead to rights, but I couldn't get the trigger to move in time- C'est La Vie-- I'd take a nice M31 like that, but as with my M12's, it "ain't for sale"__