In this paper, we present a collection of results focussing on the transport properties of doped direct-gap inverted-band highly polar III-nitride semiconductors (GaN, AlN, InN) and GaAs in the transient and steady state, calculated by using nonlinear quantum kinetic theory based on a non-equilibrium statistical ensemble formalism (NESEF). In the present paper, these results are compared with calculations using Monte Carlo modelling simulations and experimental measurements. Both n-type and p-type materials, in the presence of intermediate to high electric fields, are considered for several temperatures and carrier concentrations. The agreement between the results obtained using nonlinear quantum kinetic theory, with those of Monte Carlo calculations and experimental data is remarkably good, thus satisfactorily validating the NESEF.