Generally, a round trip airflight you book on your own is less expensive, as are hotel rooms. CCL transfers to/from the ship are about $130/pp [round trip]. If you choose to use CCL transfers, keep in mind you have to add that amount to any lower price airfare you find.
Check what CCL wants....and check what the major websites such as Orbitz [et cetera] are offering. Don't forget to add the $130 figure to air purchased independently.
Booking hotels may be a bit more problematic. Usually you can do it for less on your own. The main advantage to a hotel CCL chooses is that you know it'll have things like elevators/individual bathrooms/et cetera. You can either book independently at one of those [don't forget to add cab fare/confirm there is a shuttle from the airport to the hotel/back if you're booking independently] or research a hotel of your own at a location such as http://www.tripadvisor.com
I usually end up booking on my own as it is much cheaper. I've had good luck with hotels booking through either Priceline or Hotwire. I would check it both ways and see what the price difference is. If its close, given that you'll be in a foreign country I would book through Carnival.