Deep brain stimulation (DBS) is an established clinical therapy, and directional DBS electrode designs are now commonly used in clinical practice. Directional DBS leads have the ability to increase the therapeutic window of stimulation, but they also increase the complexity of clinical programming. Therefore, computational models of DBS have become available in clinical software tools that are designed to assist in the identification of therapeutic settings. However, the details of how the DBS model is implemented can influence the predictions of the software. The goal of this study was to compare different methods for representing directional DBS electrodes within finite element volume conductor (VC) models. We evaluated 15 different DBS VC model variants and quantified how their differences influenced estimates on the spatial extent of axonal activation from DBS. Each DBS VC model included the same representation of the brain and head, but the details of the current source and electrode contact were different for each model variant. The more complex VC models explicitly represented the DBS electrode contacts, while the more simple VC models used boundary condition approximations. The more complex VC models required 2-3 times longer to mesh, build, and solve for the DBS voltage distribution than the more simple VC models. Differences in individual axonal activation thresholds across the VC model variants were substantial (-24% to +47%). However, when comparing total activation of an axon population, or estimates of an activation volume, the differences between model variants decreased (-7% to +8%). Nonetheless, the technical details of how the electrode contact and current source are represented in the DBS VC model can directly affect estimates of the voltage distribution and electric field in the brain tissue.