Higher blocking voltage->wider drift region->lower doping concentration->higher resistance->higher Vf at a given (high) current.
So maybe they all have 0.7V Vf at 0.1A, but if you apply a 10A pulse, you will start to see the difference.
Along with higher blocking voltages lower switching speeds come also; but in such slow diodes (~2.5 micro seconds) the difference is negligible. For the fast / super fast / ultra fast (and Schottky) diodes it makes a big difference, though.
BYV26's switching speed, for example, changes dramatically; from 30ns for up to 700V parts (BYV26A..C) to 75ns for the 900 and 1100V parts (BYV26D..E).
-George