  The equation of state of asymmetric nuclear matter as well as the neutron and
proton effective masses and their partial-wave and spin-isospin decomposition
are analyzed within the Brueckner--Hartree--Fock approach. Theoretical
uncertainties for all these quantities are estimated by using several
phase-shift-equivalent nucleon-nucleon forces together with two types of
three-nucleon forces, phenomenological and microscopic. It is shown that the
choice of the three-nucleon force plays an important role above saturation
density, leading to different density dependencies of the energy per particle.
These results are compared to the standard form of the Skyrme energy-density
functional and we find that it is not possible to reproduce the BHF predictions
in the $(S,T)$ channels in symmetric and neutron matter above saturation
density, already at the level of the two-body interaction, and even more
including the three-body interaction.
