The aim of this paper is to present and compare the results of two numerical models of electron transport in the channel region of stationary plasma thrusters, namely a Monte Carlo simulation and a diffusion model. This paper extends the model of Degond et al (1998 Transp. Theory Stat. Phys. 27 203) to the case where elastic and inelastic collisions against atoms, as well as collisions with the walls are considered. After describing the extensions, we show numerical results of both models and compare them in two distinct situations. Though discrepancies between mean quantities such as the mean energy can reach a factor 2 in some cases, we show that qualitative properties of the electron population can be obtained at a reduced CPU cost by using the diffusion model. We conclude by showing that the electron population cannot be assumed Maxwellian in general, but that this assumption would lead to reasonable values for the ionization frequency if the mean energy of the population is known with reasonable accuracy.