Why \$ \frac{\mu_n}{\mu_p} \$ is very high in GaAs compared to Si or Ge
According to Chenming-Hu, Modern Semiconductor Devices for Integrated Circuits, Chapter 2:


  [...]Notice that GaAs has a much higher µn than Si (due to a smaller mn).
  Thus, higher-speed transistors can be made with GaAs, which are
  typically used in communications equipment.


Indeed, the normalized hole effective masses are comparable:


Si: 0.39
GaAs: 0.5


Whereas for the normalized electron masses:


Si: 0.26
GaAs: 0.068