  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 realistic EoS
which differ in particle content and ab-initio microscopic calculations. While
the constraining power of GW170817 is limited, stringent constraints can be
placed with approximately 10 coalescences detected by LIGO-Virgo at design
sensitivity, but only for relatively stiff EoS which are already marginally in
tension with GW170817. However, we show that even 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.
