If anything the Carnival transport will take longer since they will wait until the bus is full before heading to the pier. The taxi from the airport is a fixed cost (I think it is $25 but don't quote me. You can google on San Juan taxi costs and get your price.) So if you have more than one person in your party is can a good money saver.
Even though the ship does not depart until 10PM they will start boarding around noon. We got on as soon as they started boarding, had lunch and then got back off and visited Old San Juan. I would not recommend waiting around for the Carnival transport.
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