Light propagation in disordered media is particularly complex due to the interference effects and polarization-mixing terms. Two-dimensional systems are particularly interesting because they feature two decoupled scattering channels, with distinct spectral statistics due to the presence of polarization-coupling terms in only one of them. We here show that in one channel, Anderson localization bounds the light transport both longitudinally and transversely. In the second channel, in contrast, diffusive transport takes place independently of scatterer density. Our results open new possibilities for engineering of light transport in two-dimensional waveguides.