App note from IXYS about the pros and cons of different forward voltage drop of real shottky diodes. Link here (PDF)
According to the thermionic emission model, pure Schottky barriers exhibit a forward voltage drop, which decreases linearly as the barrier height diminishes; whereas the reverse current increases exponentially as the barrier height decreases. Consequently, there exists an optimum barrier height, which can minimize the sum of forward and reverse power dissipation for a particular application.
However, discussions with the users of Schottky diodes reveal that they do not search for the minimum of forward and reverse power dissipation but always for the minimum forward voltage drop. Values of reverse current are very rarely asked for. One must know how the Schottky diode is being applied in order to objectively select the most appropriate part.