Finite element (FE) models of the human head are important injury assessment tools but developing a high-quality, hexahedral-meshed FE head model without compromising geometric accuracy is a challenging task. Important brain features, such as the cortical folds and ventricles, were captured only in a handful of FE head models that were primarily developed from two meshing techniques, i.e., surface-based meshing with conforming elements to capture the interfacial boundaries and voxel-based meshing by converting the segmented voxels into elements with and without mesh smoothing. Despite these advancements, little knowledge existed of how similar the strain responses were between surface- and voxel-based FE head models. This study uniquely addressed this gap by presenting three anatomically detailed models - a surface-based model with conforming meshes to capture the cortical folds-subarachnoid cerebrospinal fluid and brain-ventricle interfaces, and two voxel-based models (with and without mesh smoothing) - derived from the same imaging dataset. All numerical settings in the three models were exactly the same, except for the meshes. These three models were employed to simulate head impacts. The results showed that, when calculating commonly used injury metrics, including the percentile strains below the maximum (e.g., 99 percentile strain) and the volume of brain element with the strain over certain thresholds, the responses of the three models were virtually identical. Different strain patterns existed between the surface- and the voxel-based models at the interfacial boundary (e.g., sulci and gyri in the cortex, regions adjacent to the falx and tentorium) with strain differences exceeding 0.1, but remarkable similarities were noted at the non-interfacial region. The mesh smoothing procedure marginally reduced the strain discrepancies between the voxel- and surface-based model. This study yielded new quantitative insights into the general similarity in the strain responses between the surface- and voxel-based FE head models and underscored that caution should be exercised when using the strain at the interface to predict injury.