For the sake of a high-fidelity representation of the curved surfaces characteristic of fuel pins, the standard reactor design process employs the method of collision probabilities (CP), the method of characteristics (MOC), or unstructured-grid discrete ordinates (SN) transport solvers for assembly-level calculations. In this work we provide a proof of principle using highly simplified assembly configurations that an approximate staircased representation of the fuel pin's circumference via an orthogonal mesh is accurate enough for reactor physics computations. For the purpose of comparing the performance of these approaches, we employ the orthogonal-grid SN code DORT and the lattice code DRAGON (CP and MOC) to perform k-eigenvalue-type computations for both a boiling water reactor (BWR) and pressurized water reactor (PWR) test assembly. In the framework of a computational model refinement study, the multiplication factor and the fission source distribution are computed and compared to a high-fidelity multigroup MCNP reference solution. The accuracy of the considered methods at each considered model refinement level (fidelity of curved surface representation in DORT, number of tracks in MOC, etc.) is quantified via the difference of the multiplication factor from its reference value and via the root-mean-square and maximum norm of the error in the fission source distribution. We find that for the BWR assembly DORT outperforms MOC and CP in both accuracy and computational efficiency, while for the PWR test case, MOC computes the most accurate fission source distribution but fails to compute the multiplication factor accurately.