We study the effect of particle shape on the turbulence in suspensions of spheroidal particles at volume fraction $phi = 10%$ and show how the near-wall particle dynamics deeply changes with the particle aspect ratio and how this affects the global suspension behavior. The turbulence reduces with the aspect ratio of oblate particles, leading to drag reduction with respect to the single phase flow for particles with aspect ratio $mathcal{AR}leq1/3$, when the significant reduction in Reynolds shear stress is more than the compensation by the additional stresses, induced by the solid phase. Oblate particles are found to avoid the region close to the wall, travelling parallel to it with small angular velocities, while preferentially sampling high-speed fluid in the wall region. Prolate particles, also tend to orient parallel to the wall and avoid its vicinity. Their reluctancy to rotate around spanwise axis reduce the wall-normal velocity fluctuation of the flow and therefore the turbulence Reynolds stress similar to oblates; however, they undergo rotations in wall-parallel planes which increases the additional solid stresses due to their relatively larger angular velocities compared to the oblates. These larger additional stresses compensates for the reduction in turbulence activity and leads to a wall-drag similar to that of single-phase flows. Spheres on the other hand, form a layer close to the wall with large angular velocities in spanwise direction, which increases the turbulence activity in addition to exerting the largest solid stresses on the suspension, in comparison to the other studied shapes. Spherical particles therefore increase the wall-drag with respect to the single-phase flow.