As OBFam says, you can save some money by booking your our excursions, outside of the ship.
In some ports, such as Grand Cayman, you need to tender in. Because our ship was only there for 6 hours, we thought that a ship excursion would be best. Those booked via Carnival were first off the ship at 7AM, no waiting to tender off.
Also trips purchased through the cruise line are in constant touch with the ship.
If, by some chance, there is a problem the ship knows about it and will make adjustments.
If you book on your own, you are on your own!
Seasoned cruisers will most likely make arrangements on their own.
For first timers, I would go with the ship, unless you are comfortable on your own.
Pretty much whatever you are comfortable with.