  Using a cutoff-free formulation of the coherent transport theory, we show
that the interference terms at the origin of localization strongly affect the
transport anisotropy. In contrast to the common hypothesis, we then find that
the anisotropies of incoherent and coherent diffusion are significantly
different, in particular at criticality. There, we show that the coherent
transport anisotropy is mainly determined by the properties of the
disorder-averaged effective scattering medium while the incoherent transport
contributions become irrelevant.
