When we sailed on the Triumph in February we packed our backpack.
In it we took bottled water and beach towels and lotion and stuff we'd need on our excursion. We mostly used it when we got off in St Thomas cause we had a jeep rented in St John and took the ferry over there and picked up the jeep and toured the island ourselves. We needed the towels and sun stuff for trunk bay and the water came in handy instead of buying it on the island.
On my first cruise we took a backpack on our excursions (for sign and sail cards, sunscreen, etc.). Last month we took a beach bag since Carnival started giving out towels and the beachbag had a little more storage. Other than that not much difference between the two.
Took a beachbag... also when I was on the boat I got a square shaped money container thingy to hold my cards, lisence etc.... Unfortunately the second year I tried to use it, it leaked but they are pretty handy!
When it was my husband and I packpacks. Now that we have two children, beach bag. Carnival sells a great beach bag for around $12. We bought it on our cruise before the last one. I use it not only for shore excursions, but all year long. This thing holds ALOT!!!