It will typically cost more to book through the cruise line. Also, if your tour is late the ship will wait for you. If you book independently and the tour is late getting back, the ship will not wait. Also, if you book independently you must do all the research and keep track of the time difference between the ship and local time.
Maybe for your first book through ship so you are comfortable with the routine. The ship will have a toll free number that can be called so if you book an excursion off the internet or where ever and something does happen, you can contact the ship, sometimes they can accommodate a small delay. Keep in mind that the cruise line does charge considerably more (more than double some times). We were newbies last year and this year did exactly the same tour + an additional activity because we took our daughter and we paid less than half for the three of us than what it cost us for two last year by booking with the operator direct. Also, if you find someone that gives you a great tour either through the ship, word of mouth etc - get contact info for the next time. We didn't do that last year and weren't able to connect with an awesome tour guide we had last year in St. Maarten. Look into various cruise boards like this one where more "experienced" cruisers often set up excursions and are looking for more people to go with them or will give a reference. Good luck and enjoy.