I'll try to help with St. Thomas, I haven't been to St. Maarten in a long while. I've never done a private or ship tour on St. Thomas though, I just do my own. Either to one of the beaches, or my favorite...over to St. John. It is home to the USVI National Park.
Trunk Bay is simply gorgeous. It has an underwater snorkel trail and is staffed with lifeguards from the U.S. Park Service.
Getting there and back is an adventure in itself, but is well worth it. Just allow plenty of time to get back to the ship. Here
is a link to a great FAQ article Jim C. wrote about doing it on your own.
PS. You'll need to use the BB Code option for your ticker to work.