Just got back from a 7 day trip on the Golden today - I did the St. Marteen dive excursion. It was a basic reef dive put on by Dive Safaris. I wouldn't say it was anything spectacular, however it had been about 10 years since I've been diving, so it was fun. I did the refresher course onboard with Brad from New Waves Scuba before the dive. He was very professional and it was good to clear some of the cobwebs!!
On the dive, I saw an eagle ray and there were definitely some impressive coral. I think the dive company does a shark feeding dive some days, but that was not offered by Princess as an excursion.
The people from Dive Safaris (Wade was our dive master) were awesome and everything was very well organized.
I didn't do any diving on St. Thomas so I can't speak for it.
I'd say if you have been diving in some of the other places in the Caribbean (Belize, Cozumel, Bonaire, etc.) then St. Marteen isn't spectacular - give St. Thomas a try?!!
Having done ship dives and booked my own, I prefer to book my own. The ship dives can get very crowded. Also they will pick dives sites according to time and skill level of the group (you may or may not be more advanced that the rest and get dives not to your liking).
In St Maarten a few years ago, I booked the dives outside the ship and actually ended up using the same company. Our cost was actually less. I would book direct and ask how many divers they take, tell them your preference(wreck or reef) and skill level and about getting to and from the dock to their operations.
I have heard good things about Admiralty Dive Center in St Thomas. You can call Princess and ask for the New Waves office and find out who they use at each stop and decide from there.
As much as I like to dive, and I really must like it because I dive locally in 45f water, I would probably skip St. M diving and go to the nude beach instead. On our last cruise, I dove with the ships excursion and I while the dive op tried hard, it was a very disappointing dive due to the water conditions. 5 ft of vis and a strong surge at 55ft. The wife and kids went to the beach and had a blast. Should have gone with them instead
On St. T we went with <a href=http://www.cokidive.com> Coki Beach Dive Club </a> it is the place Princess takes their discover scuba people. You can go there on your own, they will pick you up for free, and do a shore dive cheap, especially if all you need to rent are tanks and weights. This is a good option for a group of mixed divers and non-divers. Make a morning of it and take a taxi back to the ship for lunch then you will have the rest of the day to do what ever.