  In this study, we use simple performance metrics to assess the science
capabilities of future ground-based gravitational-wave detector networks --
composed of A+ or Voyager upgrades to the LIGO, Virgo, and KAGRA observatories
and proposed next generation observatories such as Cosmic Explorer and Einstein
Telescope. These metrics refer to coalescences of binary neutron stars (BNSs)
and binary black holes (BBHs) and include: (i) network detection efficiency and
detection rate of cosmological sources as a function of redshift, (ii)
signal-to-noise ratios and the accuracy with which intrinsic and extrinsic
parameters would be measured, and (iii) enabling multimessenger astronomy with
gravitational waves by accurate 3D localization and early warning alerts. We
further discuss the science enabled by the small population of rare and
extremely loud events. While imminent upgrades will provide impressive advances
in all these metrics, next generation observatories will deliver an improvement
of an order-of-magnitude or more in most metrics. In fact, a network containing
two or three such facilities will detect half of all the BNS and BBH mergers up
to a redshift of $z=1$ and $z=20$, respectively, give access to hundreds of
BNSs and ten thousand BBHs with signal-to-noise ratios exceeding 100, readily
localize hundreds to thousands of mergers to within $1\,{\rm deg^2}$ on the sky
and better than 10% in luminosity distance, respectively, and consequently,
enable mutlimessenger astronomy through follow-up surveys in the
electromagnetic spectrum several times a week. Such networks will further shed
light on potential cosmological merger populations and detect an abundance of
high-fidelity BNS and BBH signals which will allow investigations of the
high-density regime of matter at an unprecedented level and enable precision
tests of general relativity in the strong-filed regime, respectively.

General Relativity and Quantum Cosmology;Cosmology and Nongalactic Astrophysics;High Energy Astrophysical Phenomena