The transport of finite-size particles in a turbulent plane Couette flow has been studied by particle-resolved numerical simulations based on the Force Coupling Method. The influence of the deviation of particle shape from sphericity was addressed, using neutrally buoyant spheroids with aspect ratio ranging from 0.5 to 2. The particle transport was compared to the case where the inertia of spherical particles was varied by considering different particle densities (while keeping comparable Stokes number). This work has shown that close to the wall, the symmetry axis of oblate particles is almost parallel to the wall-normal direction and the major axis of prolate particles tends to align in the flow direction. Both types of particles have a kayaking type of rotation in the core region which yields homogeneous collisions. The spatial particle distribution is strongly correlated to coherent structures. However, strong deviations occur for the most inertial particles which accumulate in the near wall region. Successive stages of accumulation and release in the streaks are observed while the regeneration cycle of turbulence proceeds. The case of massless bubbles is characterized by a very strong correlation with the large scale vortices that span over the depth of the Couette gap. Even though the particles do not modify drastically the flow, they have some effect on the fluctuating energy, as suggested from the pdf. This effect is more clear for non-spherical particles compared to the spherical ones with various density ratios