A regular cab ride (not a shuttle as noted above) from FLL will definitely be more expensive and any type of transportation will be more time consuming. The trip from MIA to your hotel would probably be only 15 minutes.

Keep in mind that there is rush-hour traffic going from Miami to Ft. Lauderdale in the afternoon/early evening hours.

MIA is not a great airport, but it is an AA hub, so there may be more flight options.