This study systematically compared two hybrid deterministic/Monte Carlo transport codes, ADVANTG/MCNP and MAVRIC, in solving a difficult shielding problem for a real-world spent fuel storage cask. Both hybrid codes were developed based on the consistent adjoint driven importance sampling (CADIS) methodology but with different implementations. The dose rate distributions on the cask surface were of primary interest and their predicted results were compared with each other and with a straightforward MCNP calculation as a baseline case. Forward-Weighted CADIS was applied for optimization toward uniform statistical uncertainties for all tallies on the cask surface. Both ADVANTG/MCNP and MAVRIC achieved substantial improvements in overall computational efficiencies, especially for gamma-ray transport. Compared with the continuous-energy ADVANTG/MCNP calculations, the coarse-group MAVRIC calculations underestimated the neutron dose rates on the cask's side surface by an approximate factor of two and slightly overestimated the dose rates on the cask's top and side surfaces for fuel gamma and hardware gamma sources because of the impact of multigroup approximation. The fine-group MAVRIC calculations improved to a certain extent and the addition of continuous-energy treatment to the Monte Carlo code in the latest MAVRIC sequence greatly reduced these discrepancies. For the two continuous-energy calculations of ADVANTG/MCNP and MAVRIC, a remaining difference of approximately 30% between the neutron dose rates on the cask's side surface resulted from inconsistent use of thermal scattering treatment of hydrogen in concrete. Keywords: hybrid deterministic/Monte Carlo transport code, CADIS methodology, Spent nuclear fuel, Storage cask, Dose rate distribution