If its just the 2 of you I would say taxi. That way you don't have to wait for the cruise shuttle to fill up before they take you to the port. Taxi is probably cheaper too. The taxis have fixed prices depending on which "zone" you are going to. I think (don't quote me as its been 2 summers since I have done it) its $25 to get from the airport to the port. But there is signage letting you know at the taxi stand. You can also just ask the taxi stand person what the cost is.
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
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013