Non-spherical particles play a crucial role in industrial and geological flows, however, a comprehensive description of their rheology as a function of inertial number and asphericity remains incomplete. In this study, we examine the influence of particle shape using spheroidal particles through simulations of simple shear flow under Lees-Edwards boundary conditions, focusing on the dense flow regime at constant applied pressure. Highly flattened, i.e. oblate lentil-like, particles manifest significantly fewer contacts and lower volume fraction, compared to elongated i.e. prolate rice-like, ones with the same shape ratio. The effective friction shows a non-monotonic dependence on the aspect ratio, and slightly flattened spheroids display a negative first normal stress difference. Furthermore, non-spherical particles tend to align their major axis with the flow, and energy dissipation becomes localized along this direction. As asphericity increases, tangential forces contribute increasingly to the overall shear stress.