It depends on what you mean by "prebooking on your own". Do you mean through the cruise line or truly on your own (private tours)
Booking through the cruise line-
Waiting until you are on the ship you run the risk of not getting on the tour you want. If there is something you "have to do" then book it. If the weather is so bad they cancel you get your money back. If you don't have any idea what you want to do at a given port that you can wait until you are on board and attend the port talk.. they will give you a introduction to all the tours so you can decide.
Booking on your own-
How experienced of a cruise/traveler are you? We are experienced cruisers and unless there is a very popular tour (that fills up quickly) or its something that we can't find online to book privately, we don't book through the ship. Most of the time we wait until we get to a port and then negotiate with a local tour guide. If the weather is bad then we are not on the hook for a tour. But for something like seeing the stingrays in Grand Cayman we reserve a spot with a private tour online. MOST of the time there are private tour guides that can do a tour for less money than the ships charge BUT you lose any warranty the ship's tours may provide.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise, Magic 1/14, Freedom x 2 6/14
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013