You've picked two wonderful excursions, and I've done both.
Cave Tubing is active and super fun but a much shorter excursion than to Lamani. Typically you can pair Cave Tubing with a Zip Line or the Zoo to make a full day out of it.
Cave Tubing: First of all you will have the tender ride from the ship to the pier in Belize. When you get off the ship will be scheduled, so give yourself some time. The trip from the ship to the pier takes about 15-20 minutes. From there you connect with your tour agency and take a 45 minute bus or van ride to one of the tubing sites. You'll be geared up and get a short briefing. There is about a 30 minute walk to the entrance point on the river thru the jungle, but the path is easy and well cleared. Tubing down the river takes about 45 minutes tops. Then you have the bus ride back to the pier. It's a super fun experience and one you will enjoy, but it seems to happen quickly compared to the travel to/fro and the prep.
Lamani...one of the last mostly untouched ruin sites and one that is AMAZING. Again you tender to the pier and take a 45 minute bus ride to the river. From there you will take a river boat thru the mangroves for a good hour to Lamani. You will see all kinds of exotic wildlife and birds...we even saw a croc! The ruins are incredible and you can still climb them. The main pyramid is the tallest point in Belize and you can see for MILES in all directions from it's top. The climb DOWN is an adrenaline rush for sure! You will wander the excavated sites and see the ones still under mounds. You will encounter lots of birds and monkeys as well. Then you have the boat ride back, albeit faster as you aren't stopping to see the wildlife...and then the bus ride back to the pier. THIS IS AN ALLLL DAY EXCURSION!
Cave Tubing is a fun for the family trip and an adventure you will no doubt, enjoy and speak of for a time to come. Lamani is truly a trip back into the Mayan past, thru a largely untouched mangrove river. It just depends on what you are wanting to do. If you have younger children, I think Lamani would be too long of a trip with too many stretches of sitting.
So I've been to both...if I was going to Belize tomorrow, which would I do again?? Lamani