If shooting under older office building fluorescent lights, which give off a green cast. The FLUO matrix combats the green cast by boosting up the reds and magentas, and will lead to more natural-looking skin tones under those older fluo lights.
I don't know exactly how the FLUO matrix works, but in general white balancing only shifts the color temperature. Color temperature is based on theoretical physics. The "temperature" is the actual temperature that some object would have to be heated to in order to emit a particular spectrum of light. This works pretty well for sunlight and most lamps, because those all generate light by heating something. See wikipedia for a more detailed description.
Fluorescent lights, however, generate light differently. That means that there is no color temperature that accurately describes the color of light that they emit.
My guess would be that the FLUO matrix adjusts the color in a way that white balancing cannot. As for doing both, my guess would be that that would get you the best results, but you really ought to try and see.