We show that the recently developed self-consistent theory of Anderson localization with a position-dependent diffusion coefficient is in quantitative agreement with the supersymmetry approach up to terms of the order of 1/g 02 (with g0 the dimensionless conductance in the absence of interference effects) and with large-scale ab initio simulations of the classical wave transport in disordered waveguides, at least for g 0 ~ 0.5. In the latter case, agreement is found even in the presence of absorption. Our numerical results confirm that in open disordered media, the onset of Anderson localization can be viewed as position-dependent diffusion.