It all depends on a number of things. First, if you book a shore excursion off the ship and dont make it back in time, or get injured or sick, you are on your own. If you purchase the ship's shore excursions, they will make sure you make it back to the ship in all instances. Also, the cruise line requires tour providers to carry insurance for your protection.
That said, generally there is asavings if you book a shore excursion off the ship and you would generally travel in smaller groups and basically get more for less.
If you, or anyone in your party, is "at risk" such as with heart problems, medical problems, overweight, then I would strongly suggest that you take a ship's tour.
Hello, while in Grand Cayman last year on the Voyager, we booked the snorkel/stingray excursion through Captain Marvin (captainmarvins.com)after reading so much positive feedback on these message boards! They were very accomodating to us and our 4 children. The boat and crew were wonderful too. Our boat was much smaller than the others hired out by the cruiselines; in fact we could see the folks just packed in like sardines on those! The crew got into the water and really helped the kids, picked up the stingrays for them, etc... we all really enjoyed it. As for pricing, it saved us a little money since there were 6 of us. There were no worries about getting back on time, they were very aware of timing in order for us to get in the 3 snorkeling stops they had promised.
It was very crowded in port in Grand Cayman that day, and the only headache we had was having to wait to tender in. RCCL tells you they will give out the first tender tickets to passengers who booked excursions through them, so I was a little concerned we wouldn't make it out in time. Due to advice I found on the message boards, I sent my husband down to get in line for tender tickets very early anyway. It became so crowded that the staff was practically just throwing the tickets out to everyone, so that worked out okay and we made it in time. I would definately give yourself 2 hours or so from the time the ship is scheduled to dock, to your excursion. I do also agree with the prior posts in that if there any medical concerns, etc....it probably be better just to book through RCCL though. Hope this helps you.
llfisher, we also booked the dolphin swim on our own in Cozumel. We had a difficult time getting a taxi to the park (Chakanaab Park, I think it is called), but managed to get there with the other million people there that day! (it was the Easter holiday plus Spring Break week, and the park folks told me this was the crowdest they could ever remember being...)
If you book on your own (they also have a web site)there isn't any age requirement, and at the time our youngest was only 6. If we were to book this same excursion thru RCCL, there was an age req. of 8 years or older. Pricewise, I don't think we saved much, it was more the age thing. The kids all wanted to do this, and we couldn't leave the yougest one out (she was the most excited).
So here I was standing with this group of 14 or so, on this wire plank in the dolphin tank, everyone wearing lifejackets, but my 6 and 8 year olds couldn't stand up without floating away! (The water was almost up to armpits). So I basically had to hold the back of their lifevests, and also manage to keep myself on the plank with my toes. It was very educational though, you get to pet the dolphin on the belly as the trainer brings them up to you, and they take a really cute photo that you can purchase. Depending on the ages of your group, just some food for thought. Hope this is helpful.