There's really no absolute answer to this other than this.
Research what you're interested in at the ports you are going to be stopping at. There are excursions I would never book outside of
DCL. Any tour that takes you very far from port would probably be a thru DCL excursion. The reason being, if you are late getting back, the ship will wait for the tour to return if it's booked thru the cruise line. They will not wait for others just being late returning. Also you are absolutely guaranteed a refund if it's thru DCL. It's up to a tour operator if you book direct. We did have a near miss once with this. I've been on both the Eastern and Western.
All I can tell you is what we did.
-St. Maarten, the island and semi-subersible tour. We rode in very nice airconditioned buses to the SeaWorld Explorer semi-submersibles and it was very nice. I don't think I'd do that myself, as it was quite far to get there.
-St. Thomas, we did the Coral World and island tour. We're doing this ourselves in December and going right to Coral World. I wouldn't do that thru DCL again, it's not too far and there are ready taxis all over to run people back and forth. Coral World itself is worth going over for it is very nice. Going up to the highest point of the island was ok, but no big thrill. Better to do the Paradise Point Tramway. When we did the DCL tour the open air bus we were in broke down on the way back to the port. Thankfully, it wasn't anything terminal, and we did make it back, but the driver did call ahead to warn them and they confirmed they'd wait for us if we were late.
-Key West. You really don't need a tour to travel here, you can walk from the port to the southernmost point all by yourselves, which is a long walk, or take the trolley which is more like an unlimited shuttle service around the island with narrative. You can get on/off trolleys wherever you want. You can get discounted tickets right from the operator here for the trolley:
http://shophta.com/acb/stores/15/product1.asp?SID=15&Product_ID=13&kc=y Key West is also a good place to pick up anything you want to bring snack beverage wise onboard instead of before sailing on the Western. There's a grocery store about 5 or so blcoks down east off Duvall you can see it from the corner.
-Grand Cayman. We took the tour to the Turtle Farm, Hell and Stingray City and enjoyed this tour a lot. Yes, Hell is a tourist trap, but fascinating for the little time you spend there and you can send yourself a postcard from Hell.

Kids love the turtles, and of course the Stingrays are not to be missed. We didn't go out on that big or crowded a boat. Maybe the stingray only excursion thru DCL is more crowded. Had lots of time to interact with them and were quite satisfied with our time spent there. if you're only interested in Stingrays, Captain Marvins is the one recommended over and over here.
Note, right now Grand Cayman is still recovering from Hurricane Ivan; it won't be open to cruise ships until sometime in November if not later, and a lot of the island is still many months till recovery, if not longer. Some resorts are saying 6 months and some no longer even exist.
-Cozumel. We did the San Gervasio ruins, island tour, and time at Playa Sol. Having never visited ruins anywhere before, it was interesting. The real ruins are over at Tulum, but I would warn, it's an all day excursion, and the ride to/from can be rough and long, small kids won't be too happy. The island tour was ok, the beaches on the ocean side are cool with all the rock formations. The time at Playa Sol was ok. One thing about Cozumel, LOTS of pushy salespeople everywhere. Even going in and out of Playa Sol. All that said, next tiem we're there, the two of us are going to do the Tulum tour. Personally, for kids, Chakanaab sounds like the most fun.
-Nassau. You can book almost anything yourselves here if you want to . You can definitely go visit Atlantis on your own, the Pirate Museum and some others. For Atlantis, to use their water recreation, you need to have a room booked at Atlantis or Comfort Suites which is right next door. To tour the Atlantis resort otherwise, you can get a wristband for walking access to everywhere right as you get there. The only bad excursion I've heard of here was the glass bottom boat tour.