Why do electrons move faster than holes in a semiconductor?
Perhaps it might be easier to start at the energy state.

Free electrons (those moving from one atom to another) are in the conduction band and holes (the lack of an electron in an orbit) are in the valence band (same link).

The conduction band is at a higher energy level than the valence band and that means that things move faster. More interestingly, for an electron to move from the conduction band to the valence band (and fill the hole) it must lose some energy.

From a more intuitive perspective, when a hole appears in a valence orbit, not all possible electrons will drop into it; quite a number will pass by until an electron that has (crucially) lost sufficient energy to move into a lower energy band will fill the hole.

When said electron left an orbit (creating a hole), it was because it had energy added perhaps by a collision or even just from heat (otherwise it could not take on a higher energy location in the conduction band). Only when it has used up that energy (by moving or maybe colliding with another object which can eject a photon - this means the electron has lost 1 photon worth of energy) can it lose that extra energy and drop into the valence band.

This is perhaps explained by a more detailed look at energy levels