In former investigations on the spatial relaxation of the electron component of weakly ionized plasmas a considerable spectrum of distinct spatial structures has been found in the velocity distribution function as well as in various macroscopic quantities of the electrons. These results have been mainly obtained by solving the spatially inhomogeneous electron Boltzmann equation considering the action of uniform electric fields and the impact of elastic and inelastic collisions of the electrons with the gas atoms. To verify these partly unexpected results on the complex structure formation, analogous Monte Carlo simulations were performed now for a helium plasma at various reduced electric field strengths. Detailed comparisons were made between the results of the two independent kinetic approaches with respect to the spatial evolution of the velocity distribution function as well as of associated macroscopic quantities. Good agreement was generally found, thus confirming the earlier results on the complex spatial relaxation structures.