This study presents a comparison of isotropic and anisotropic filtered Two Fluid Model (fTFM) closures for drag and mesoscale solids stresses. Anisotropic modelling of drag is important to correctly predict the drag correction in directions not aligned with gravity, while anisotropic stress modelling predicts the deviatoric component of the mesoscale stress tensor with much higher accuracy than closures based on the conventionally employed Boussinesq approximation. Comparisons to a highly computationally expensive resolved simulation showed that the anisotropic stress model had the largest positive effect on model accuracy. Clear improvements relative to the isotropic model were observed for all flow variables, including reaction rates. Anisotropic drag modelling had a smaller, albeit still significant effect. In general, the good performance of the newly proposed anisotropic fTFM closures observed in this study serves as a clear recommendation for future study in this direction.