A fully quantum theory of phonon-limited electron transport in semiconductors is applied to a homogeneous steady-state situation to investigate the difference between quantum results and the results of a semiclassical theory. The Wigner function is used for the quantum approach, and the Monte Carlo simulations are performed in both semiclassical and quantum theories. In the considered case, hot-electron transport in a simple silicon model at 77 K, very little difference has been found since collisional broadening changes the possible final states of the electronic transitions without altering in a significan way the total scattering rate and therefore the momentum relaxation efficiency of phonon scattering.