The rotational friction factors are rarely observed directly.  Rather, one measures the exponential rotational relaxation(s) in response to an orienting force (such as flow, applied electric field, etc.).  The time constant for relaxation of the axial direction vector is
whereas that for the equatorial direction vectors is
These time constants can differ significantly when the axial ratio  deviates significantly from 1, especially for prolate spheroids.  Experimental methods for measuring these time constants include fluorescence anisotropy, NMR, flow birefringence and dielectric spectroscopy.
It may seem paradoxical that  involves .  This arises because re-orientations of the axial direction vector occur through rotations about the perpendicular axes, i.e., about the equatorial axes.  Similar reasoning pertains to .