The Molten Salt Fast Reactor (MSFR) has recently been chosen as the reference circulating-fuel Molten Salt Reactor design in the framework of the Generation IV International Forum. Different from most of the Molten Salt Reactor designs developed and proposed in the past, the MSFR is featured by a fast neutron spectrum. On one hand, this choice leads to a simplified core (no graphite is present) and to improved characteristics in terms of breeding and/or transuranic burning. On the other hand, the removal of graphite leads to a significantly different behavior in terms of both core neutronics and dynamics. In view of the ongoing development of dedicated tools for the MSFR transient simulation, it is useful: 1) to accurately determine the core feedback coefficients, for lumped models and to get an insight into the reactor safety features; and 2) to analyze the degree of approximation related to the use of deterministic multi-group transport and diffusion approaches, in case of multi-dimensional models. The present paper compares the results obtained by means of the deterministic code ERANOS 2.2N with those obtained through the Monte Carlo code PSG2/SERPENT, for different fuel cycle strategies. In particular, the comparison is based on the capability to reproduce nominal reactivity, feedback coefficients, spectra and flux profiles. In the light of these results, the capability of a simple few-group diffusion model to deal with the MSFR neutronics is preliminarily assessed. Such model has been set up by means of the general-purpose finite-element COMSOL Multiphysics software. It is of interest for a subsequent development of multi-physics models able to reproduce the peculiar MSFR transient behavior.