Of all the cruises I've been on, I've only taken one ship-sponsored tour. Needles to say, it was my last. And I agree with the others when they say they are a "rip".
The cost is well in excess of what you can get on your own. The tours are crowded. The busses spend too much time dropping you off at tacky and over-priced shopping areas, in which the cruise lines get a "kick back" from the vendors.
I have been on dozens of private tours and have always returned to the ship well in advance of the ship-sponsored tours.
What I like to do is to charter a taxi, tell the driver what I want to see, plus ask for recommendations of other sites. I make sure he speaks English, and negotite the cost prior to arranging the tour. I pay for half the cost up front, and the balance at the end of the trip. The driver takes me where I want to go, and most importantly avoids the places I have no interest in seeing (cheap souviner stands). I stay at each place as long or as short as I desire. I beat the crowds (not part of a large group). When I go to the beach, the driver will wait several hours for me (that is why I only pay half up front).
When I return to dinner, the other guests are often envious of me when I share my experiences for the day vs. their's. I ended up seeing more, in less time, paid far less, avoided crowds, and overall had a more enjoyable trip.
There may a few ports (Venezuela for example), where you would not want to venture out on your own, put it is perfectly safe in all the Caribbean islands.
I am not a bully-pulpit for the cruise lines. Do consider go out on your own. You're not only save alot of money, you'll have a better time and see more in less time.