Fibermesh and steel reinforcing (bars or mesh) perform different functions.
Fibermesh helps prevent early age plastic shrinkage cracks long enough to saw cut some control joints but once a crack or cut occurs, fiber doesn't provide and strength.
Rebar and mesh don't do much to prevent cracks but they hold the cracks and/or sawcut joints together. Steel reinforcing doesn't do much to resist loads applied to the slab either - the subgrade does that.
You could use fiber and steel but given a choice, I'd go with steel. If you don't want to risk random cracks, you are going to have to sawcut anyway. Once the sawcuts are in, the benefits of fiber are moot. The steel reinforcing will still hold everything together.
To answer your original question regarding bars or mesh, rebar is the better choice. The extra steel section isn't necessary but the rigidity of the bars themselves will span between supports better ensuring that the reinforcing remains in the center of the slab rather than lying on the bottom.