We have been on about 20 cruises. We have had some great experiences booking our own tours and other times it has been misses. In Grand Cayman we tried getting to Stingray city on our own and ended up in an area with huge waves barely able to get out of the boat. My daughter was about 2 at the time to the excursion ended up being nothing like the add on TV.
We did booked a kayak tour and saved 30% off the ship rate. We were on the same bus as if we had booked direct. In St Thomas we have ended up on a sailing boat with just the 3 of us with a provate guide. We did Dunn River Falls on our own and had a great time and discovered a local market off the beaten path. I think the bottom line is if you want to book on your own you must be a bit flexible and you will end up having a great time for less. If you are going to worry about the missing the boat self tours are probably not for you. We have also used public transportation and had lots of fun. In Barbados for example the bus driver flagged down another bus to get us to our destination more quickly. Doing your homework always pays off. We have found great beaches, enjoyed food and drink with locals and really gotten a feel for the country by venturing away from the arranged tourst. The cruise ships have done their homework and do know what tours people enjoy so if you don't want the hassle of hours of research this is an easy way to get a teaste of the country.