I have yet to use a shuttle in FLL. The cab ride is easy and less expensive for two people.
When using the cab the driver always loads the bags in the trunk and unloads them at the ship. From there the luggage handlers take them and put them on board. Not really any more luggage handling than you would have with the cruise line.
One time, shortly after 9/11, we did have to wait about ten minutes at the port entry because they were checking the cabs and other shuttles. Otherwise we've had little or no wait.
It really is a matter of preference. If you like to use the cruise line shuttle then go for it.