First of all, that's a great gun. It has the Invector+ bore but some additional features as well. I've spent a lot of range time with that gun, including time with the design engineer for Browning that lead the team that developed that gun and the Winchester SX3. We shot the Full Strut choke that Browning recommends for that gun. It has a .640 exit diameter and does an excellent job with a variety of shotshells, including Hevi-13 and others. I shoot the SSX through that gun, it has very different internal geometry from the Browning Full Strut but a similar exit diameter, .643 and it does an excellent job as well.
You have a great choice of brands and designs and it's not all about the exit diameter but more about how the manufacturer designs his choke tubes. That's why a .665 may perform very well in one brand and a .675, ,680, .640 or .643 in another brand may perform equally well.
While I've shot a number of 3.5" shells though that gun, I much prefer the 3" and find that they'll do all that's necessary to cleanly kill a bird at all reasonable ranges. I like and shoot Hevi-13 shells both in competition and for hunting and use mostly #6 shot.
No matter what you choose I know you'll enjoy that gun.
Thanks,
Clark