Official city-data Bristol resident reporting for duty!
It's difficult to say why, historically, the Lake Winnipesaukee area developed into a more "upscale" resort region. I imagine that at one point in time it probably had to do with ease of access (via rail etc.) from the Boston area, as well as the appeal and promotion of the lake itself, being the largest in the region.
However, I would make a significant distinction between Bristol and towns like Franklin. Although Bristol does have a couple of old abandoned mills, I certainly would not lump it into the "dying mill town" category, in particular because the town has historically relied less on industry than places like Franklin, and much moreso on tourism. After all, Franklin doesn't have a big lake in it.
The most important difference between Bristol and say, Meredith, is that Bristol's town center is not situated immediately on the lakeshore. The prime real estate is a couple of miles away from the town center, so the heart of town has not benefitted as much from the economic advantages of lakeside establishments. Even so, the town can get quite hopping in the summer months. There's a tremendous amount of restaurants for such a small town.
Frankly, I think Bristol is slowly but surely becoming a more attractive town to live in and visit. It may not be as polished as Meredith or Wolfeboro, but that's part of the appeal for a lot of people. It's a more "genuine" town in some respects, and Newfound is less crowded than Winnipesuakee (not to mention cleaner!) As a local, I can attest that there is a somewhat more "provincial" mindest here than in other towns in the Lakes Region, but on the other hand it has been spared from excessive yuppification.
In this local's opinion, Bristol is not perfect but it really does present a nice balance of a scenic resort area and an authentic small NH town. It's miles of ahead of Franklin and other towns that are stuck in decline.