We just returned from a week at the Kauai Marriott. While it is an older property, I find it quite enjoyable. The gardens are beautiful and the pool may well be the largest in Hawaii. The beach is right in front of the hotel and we spent most of our time there. I love looking across the bay at the mountains--to me it's very relaxing.
We stay on the Vacation Club side of the property, so I can't vouch for the condition of hotel rooms.
There are a couple of good restaurants on property and several others within walking distance.
The resort is by the airport in Lihue, centrally located between both the Poipu and Hanalei sides of the island. I find it a good location for sightseeing.
I haven't been to the Sheraton, so I can't compare the two. As much as I like the Marriott resort, I don't think it compares favorably to St. Regis in either quality or price. I do agree that the Princeville area tends to be a little rainy and probably cooler.