The chief advantage over direct amperometry is that the magnitude of the measured current is of interest only as an indicator.  Thus, factors that are of critical importance to quantitative amperometry, such as the surface area of the working electrode, completely disappear from amperometric titrations.
The chief advantage over other types of titration is the selectivity offered by the electrode potential, as well as by the choice of titrant.  For instance, lead ion is reduced at a potential of -0.60 V (relative to the saturated calomel electrode), while zinc ions are not; this allows the determination of lead in the presence of zinc.  Clearly this advantage depends entirely on the other species present in the sample.