  Gravitational-wave measurements of the tidal deformability in neutron-star
binary coalescences can be used to infer the still unknown equation of state
(EoS) of dense matter above the nuclear saturation density. By employing a
Bayesian-ranking test we quantify the ability of current and future
gravitational-wave observations to discriminate among families of
nuclear-physics based EoS which differ in particle content and ab-initio
microscopic calculations. While the constraining power of GW170817 is limited,
we show that even twenty coalescences detected by LIGO-Virgo at design
sensitivity are not enough to discriminate between EoS with similar softness
but distinct microphysics. However, just a single detection with a
third-generation detector such as the Einstein Telescope or Cosmic Explorer
will rule out several families of EoS with very strong statistical
significance, and can discriminate among models which feature similar softness,
hence constraining the properties of nuclear matter to unprecedented levels.
