When I go to the islands with the whole family, my first choice is Maui. When I go for alone time with Mrs. tigre, our top choice is Kauai. I personally would choose to spend the bulk of your time at Princeville. The Sheraton Maui is a very nice hotel, but it doesn't compare to the St. Regis.
For one day of golf and spa, the St. Regis is the clear choice for that day. Both have good pools and beach. I'd prefer lounging at the St. Regis pool. While snorkeling is fine there too, the snorkeling at the Sheraton's Black Rock wins. The North Shore of Kauai has the best hiking, including the mother of all Hawaiian hikes in the Kalalau Trail (at least do the 4 mile trek to the inland waterfall - to go further than the beach, you'd need a permit).
A helicopter tour would be much better on Kauai. I've done the zipline at Princeville Ranch in Kauai, which was very cool, but have yet to do it in Maui.
The biggest issue with Princeville is that your trip is in November. I have only been there in the summer and even then the weather can be a bit more sketchy. It can rain almost non-stop for days on Kauai's North Shore in the winter. That won't happen on Kaanapali Beach.