I always use a taxi to the ship. It is much less hassle and more efficient. You can make sure that your luggage gets on the ship and you can time your arrival at the crusie terminal to one of the first to board the ship.
Even if it cost more, it is worth it. However, assuming it is just your two, it will be less expensive to take a taxi to boot in MIA or FLL.
I always prefer private transportation because the shuttle takes longer. You have to wait for the shuttle busses to fill up, then all the luggage is stowed and by then I could already be at the port. Plus you aren't getting to the port at exactly the same time as a shuttle group, often making check-in quicker.
I vote for taxi, we generally go in a nite early and stay at a hotel that has a shuttle, this gets us to the hotel, and then gets us to the ship the next morning, and then we take a taxi from the ship to the airport for the return trip.
If you are arriving in Fort Lauderdale and going to Port Everglades, MOST DEFINITELY just grab a cab. The cost for two of you will be less than the total cost for the shuttle service and as everyone has said, It is much faster and efficient!