We compare two competing relativistic approaches to the N-body simulation of the Universe large-scale structure. To this end, employing the corresponding alternative computer codes (“gevolution” and “screening”), we conduct a series of cosmological simulations in boxes of different sizes and calculate the power spectra of the scalar perturbation Φ, the frame-dragging vector potential B and the difference between scalar modes $\chi =\Phi -\Psi$. We demonstrate that the corresponding power spectra are in very good agreement between the compared schemes. For example, the relative difference of the power spectra for Φ is 0.04% maximum. Since the perturbed Einstein equations have much simpler form in the screening approach, the simulation with this code consumes less computational time, saving almost 40% of CPU hours.