Using as a benchmark the porous flow in a square array of solid or permeable cylindrical obstacles, we evaluate the numerical performance of the two-relaxation-time lattice Boltzmann method (TRT–LBM) and the linear finite element method (FEM). We analyze the bulk, boundary and interface properties of the Brinkman-based schemes in staircase discretization on the voxel-type grids typical of porous media simulations. The effect of flow regime, grid resolution, and TRT collision degree of freedom Λ is assessed. In coarse meshes, the TRT may outperform the FEM by properly selecting Λ. Further, FEM is more oscillatory, a defect virtually suppressed in TRT with an improved strategy IBF and implicit accommodation of interface/boundary layers.