FWIW, I have a similar gun, Browning Gold. I patterned it a few years back with a .680 Trulock 'Precision Hunter' choke. Worked fine with T shot & #4 buck.
I ended up choosing the .680 after talking with G Trulock in GA & mentioning shooting mostly the T shot with some #4 buck. That's what he steered me to.
As you may know some bores are tighter than others, before you get anywhere near the choke. The modern Brownings, like Winchester are 'back-bored', which is slightly larger diameter. That being the case, chokes of a certain constriction can interact differently than say a smaller bored Benelli gun.
I've also used my .680 just fine on turkey with #6 Remington HD ammo.