Hardest used? The 30" barreled BSS, no doubt. It gets knocked around in the duckayak, in and out of duck blinds, and in duck boats of all descriptions. Pretty rough life for a double.
Most shot while hunting? That's been a toss up for the last couple years between the 12 ga. 32" barreled BE grade 1918 Fox, and the 30" barreled .410 Dickinson, which gets service regularly in the dove and quail fields.
My faithful for 15 yrs. 30" barreled 687 SPII Sporting 20 gauge has been neglected this year. But ............if we pull the trip together to Cordoba for early next August, we'll make up for it.
I'm sorry, but I can't pick one specific double, as I tailor the gun to the type hunting, and they vary so much.
SRH
I'm not the sharpest knife in the drawer, but the more I think about the OP's question, I think he was asking the one that has been used the most on game. I was just a little too dense to understand it initially.
There is no contest there. The 687 SPII Sporting has been fired around 10,000 times, at game. It's probably the most proven gun I will ever own.
SRH