Having stayed at both on an engagement trip, I will agree with the other posters that the St. Regis is definitely the place to go for a non-kids vacation. The Hyatt was great as well, and I will definitely go back, but it was a ton of families with kids when we went in July. The St. Regis had many more couples/honeymooners which we both liked better without having kids of our own.
Depending on the length of your stay though, it could be worth it to stay at both. We had 7 nights and were really glad that we stayed at both. The weather at the Hyatt was sunny everyday, which was a nice contrast from the rain we experienced on 2 out of our 4 nights at the St. Regis. I've also heard of people experiencing a lot of rain each day of their vacation at the St. Regis which almost never happens at the Hyatt. This also gave us a nice variety of activities.
Either way, I'm sure you'll have a great trip. It was definitely one of our favorites.