Is there any practical use for that characteristic? I mean, are there situations in real life in which it is desirable/useful to have a logarithmic (as opposed to linear) voltage drop?No. The voltage across a diode is a logarithmic function of the current.
Here's a typical curve of diode forward voltage versus current.
My simulation gave 490mV and 575mV drop respectively for the two diodes.
Maybe metrology or normalization of certain signals?