In the present work, an assessment of the Neutronic Benchmark of the Molten Salt Fast Reactor (MSFR) was performed using mesh based Monte Carlo Neutron Transport (MCNT) calculations with numerical uncertainty quantification due to discretization in neutronic parameters. Calculations with Constructive Solid Geometry (CSG) models where made as a baseline for the developed mesh based models. The numerical uncertainty given by the mesh utilization is evaluated using an extended version of the Grid Convergence Index (GCI). The fuel salt reprocessing is evaluated regarding a constant reprocessing rate. The fuel salt inventory variation with time for the developed models (CSG and meshed) is presented. The differences caused by the discretization procedure are noticeable, which shows that mesh based MCNT require careful mesh sensitivity evaluation and further validation.