Hopefully AA will hold its own, because FLL-LAX is actually a pretty strong F route, especially since the majority of the Miami area's big corporations are located in the FLL area, not MIA area. Sort of like LAX-BNA, which has held very well against WN over the years thanks to high F demand.
Though I will says, jetBlue is averaging loads of something like 155-160 (on a 162-seat plane) on FLL-LGB, and yields have been extraordinary.