The Sodium Fast Reactor is one of the most technologically developed Gen-IV reactors, which can close the nuclear fuel cycle. Its criticality safety directly depends on the sodium void effect and Doppler constant. Hence the knowledge of their local distribution is important. These coefficients can be mapped by deterministic or Monte Carlo codes, where the latter provide higher modeling accuracy, but are also strongly computer demanding and subject to stochastic noise issues. In this study, the void effect and Doppler constant have been enumerated for the ESFR core by Serpent2 and ERANOS2 codes, preserving a six-batch operation scheme. The Serpent code was coupled to the Python script BBP to simulate batch-wise operation in a radially infinite inner core configuration; the ERANOS code was applied to the whole core geometry and the batch-wise operation was simulated by the EQL3D routine. Sodium void effect and Doppler constant spatial maps with different levels of refinement were produced, as well as the time evolution of the integral coefficients during the transition from initial cycle to equilibrium cycle. Both codes indicate deterioration of these coefficients during the transition. The equilibrium cycle performance of the inner core zone from the ERANOS calculation was compared with Serpent results and they showed reasonable agreement. For very fine mapping, the Monte Carlo method employed was computationally very demanding and the enumerated effect was lower than the stochastic noise. In general, the Serpent model practically excludes modeling assumptions and produces reliable results for reasonably sized maps, which can be combined if needed with the high spatial resolution results obtained by ERANOS simulations.