I recently returned from a one week stay at each property.
I have to say that I loved the Princeville resort. It only has about 140 units, so it's much smaller and intimate feeling - I think about 8 buildings spread out, with each building only having 3 floors. This means that your own unit is that much more accessible and there was plenty of parking available. Also - pools & barbecues were very accessible - I preferred being in the ground level unit so I could just walk out from my room to the pool & barbecue. Also - the restaurant on property, Nanea, was one of the best meals I had the entire time on either island. The biggest downside, of course, is no direct beach access, but the north shore of Kauai has so many beautiful beaches that it wasn't a huge detraction. I personally was not a huge fan of the St Regis beach - it's completely manmade & the layer of sand is kind of thin, and faces into Hanalei bay, but without any of the perks of going to Hanalei bay proper (no kayaks or paddle boards to rent, etc). If you do go to Kauai, I highly recommend going to Anini beach - it's beautiful & picturesque with a lot of trees reaching right over the ocean. If you're into hiking, I personally feel that Kauai had much more to offer than Maui in that respect.
The Ka'anapali resort is great too, especially the beach access as it's one of the nicest beaches on Maui. I found the restaurant to be so-so & expensive in terms of relative value. Also, I found parking to be a huge hassle (stayed in the North tower). The spaces are almost all compact, but more than half of the guests have SUV's so they inevitably end up taking 2 spaces. Also, unless you're staying very close the elevators, the walk from the parking lot to some of the rooms is ridiculously long. However, for water activities Maui is definitely better.
We found our rooms at both resorts to be beautiful and well maintained, and the staff were exceptionally pleasant and helpful at both.
All in all - if you can swing it, I'd say visit both! But if not, Kauai & Princeville still take a special place in my heart. It's too bad Princeville is a voluntary resort...