We use three-dimensional contact dynamics simulations to analyze the rheology of polydisperse packings of spherical particles subjected to simple shearing. The macroscopic and microstructural properties of several packings are analyzed as a function of their size span (from nearly monodisperse to highly polydisperse). Consistently with previous two-dimensional simulations, we find that the shear strength is independent of the size span despite the increase of packing fraction with size polydispersity. At the micro-scale, we analyze the particle connectivity, force transmission and the corresponding anisotropies of the contact and force networks. We show that force distributions become increasingly broader as the size span increases. In particular, stronger forces are captured by larger particles, which are also better connected compared to smaller ones. As a consequence, the contact anisotropy declines with size span, whereas the force anisotropy increases. The additive compensation of these two opposite trends leads to the independence of the shear strength from size polydispersity.