I picked up my first BNW victory with them, also my first King victory. Diplomatic, and could've had culture in another 4 turns. I played a huge map, continents, and had Monte, Shaka, Khan, and Poland as neighbors. I figured it was going to be a rough go, but I had a great starting spot for my capital and my pathfinders were able to pop enough culture to finish out the liberty tree and faith to found a religion. I stayed with 5 cities and kept an average military. Amazingly, despite my aggressive neighbors, I never got DoW'd the entire game (a civ first for me in all my years of playing). My victory game in game standard speed year 2006 AD.
The entire game I felt in complete control, at any point I could have raised an army and taken out the competition, I had a healthy tech lead on most.
Compared to other recent BNW games I give the Shoshone this - decent civ, awesome start bias, and their ability to settle more land and choose their bonuses with pathfinders means they have a great base to start with. And it's incredibly adaptable, had I simply made my pathfinders in to composite bows early on, I could've taken out Monte and Shaka.
Other thoughts, I wonder if the civ bonus of increased unit strength in your own borders factors into whether civs will declare on you. By no means was I the strongest civ militarily, and as the game dragged on, I purposely stopped expanding and upgrading troops just to see if I could entice a DoW, no luck.