Cottonwood has more of a local vibe; low-key place with a couple of great pools, close to Buena Vista. It's a little worn, but I find that to be part of the charm. I prefer going here.
Princeton is waaayy more ritzy, and expensive. It does, however, have some nice amenities such as a steam room and cold plunge. It's a whole different experience.
It really depends on what you prefer.