From the wording of your question, it isn't clear if you are referring to a lead-free flux for a surface mount application (solder paste flux), a wave soldering application (liquid flux) or a hand soldering application (cored wire flux), but in each case, at least to some degree, there is certainly value in utilizing fluxes are known to be lead-free capable.
Although some fluxes that had originally had been designed for leaded applications may work acceptablyinlead-free applications, there are many new fluxes on the market today that were designed specifically for lead-free soldering processes. These fluxes represent improvements over traditional fluxes in terms of solderability.
Since lead-free alloys melt at higher temperatures and don't spread as easily as leaded alloys, lead-free compatible fluxes tend to have higher activity and higher heat stability than traditional fluxes. This gives most users reason enough to make the switch to a newer flux that was designed specifically for lead-free processes.