I'll be able to help you out on this one after I return from a POA cruise I am taking in October. We have reserved rental cars for all islands and are not taking any excursions through the ship.
Our first cruise was a Celebrity about 6 years ago that went to Key West, Ocho Rios, Cozumel and Grand Cayman. We booked shore exursions through the ship and were very pleased with all of them - we felt it was the best way to see places when we only had a day at each stop.
On a Bermuda cruise the following year, we were very disappointed with the excursions we booked through the ship and discovered that there were plenty of taxi's waiting at the dock that could take you places you ordinarily would not see through through a shore excursion, which is what gave us the idea of not booking excursions for this POA. SInce we were in port for several days in Bermuda, we found better things to do using local transportation than we did with the shore excursions.
This was re-encorced on a three day RCI cruise to the Bahamas last year - the shore excursions we booked ended up being cancelled due to rough water and we were stuck walking around in town on one of the dates. Had we been better prepared and researched what was available on the island before hand, we could have done found our way around better.
I can only tell you that for Hawaii, we researched things to do and see (using the excursion guide from the cruise line, too) and found we could rent a car and see these things on our own time table. Additionally, one of our party recently had back surgery and we felt that if we booked a shore excursion and she isn't felling well, she would be stuck for hours on the excursion - when if we had a car, we can take her back to the ship if she isn't feeling well.
I can tell you we booked a luau in Maui and saved about $24 per person rather than booking a luau on the ship.