Mobility of electrons vs holes in semiconductors (intrinsic vs extrinsic)

I was reading my class notes and it was written that electrons are more mobile than holes because the effective mass of electrons are lower than that of holes. (μ=eτ/m*)

I checked online to find the relative effective masses of electrons vs holes and in intrinsic semiconductors (like Ge and Si) and found out that the effective mass of electrons are higher than that of holes. So is the relative mobility of electrons still higher than holes in this case (and the collision time constant for electrons much higher than holes to compensate for the lesser effective mass)?

Besides I came across an article on this site which explains that since mobility of electrons are due to electrons that move in the conduction band which is higher than holes as they are much freer than the electrons which move in the valence band (whose movements dictates the movement of holes) due to columbic attraction of the electrons and holes. How can I relate this answer to effective mass?