Two-dimensional maximum entropy closure and various standard one-dimensiona
l closures in flux-limited neutrino diffusion and two-moment transport are
compared against direct numerical solutions of the neutrino Boltzmann equat
ion. The approximate transport based on particular closures of the moment e
quations is rated by testing so-called weak equivalence of the first three
moments of the neutrino radiation field. Additionally we consider strong eq
uivalence of the maximum entropy angular model distribution. Our calculatio
ns are performed on two different matter backgrounds and involve several ne
utrino energies. As an alternative multiple energy test we look at the beha
vior of spectral and energy-averaged Eddington factors. Among the closures
considered, two-dimensional maximum entropy closure is found to overall app
roximate most closely the full transport solutions.