In a farm situation I have operated both conventional and hydrostatic driven machinery. From my experience a hydrostatic drive, although it has its pluses such as near infinite speed selection, is very hard of fuel (required a larger engine). Almost 110%-115% greater fuel use than conventional drive. Depending on job being done.
But the machinery I'm thinking of is from the late 1990's. I know that the earlier designs were even more inefficient, in the 120% worse range. But in certain farm applications, where you need precise speed control, hydrostatic drive is a huge bonus.
In farm machinery applications, a speed range is gear selected. The engine speed can vary, but is normally fixed at a specific speed, to prevent lugging the engine or stressing the hydrostatic pumps and motors. The speed variation is obtained by adjusting the fluid volume flow. I wouldn't know if operation and performance is different on newer equipment though.