  We consider stellar-origin black hole binaries, which are among the main
astrophysical sources for next generation gravitational wave (GW) detectors
such as the Einstein Telescope (ET) and Cosmic Explorer (CE). Using population
models calibrated with the most recent LIGO/Virgo results from O3b run, we show
that ET and CE will be capable of detecting tens of thousands of such sources
(and virtually all of those present in our past light cone up to $z\lesssim
0.7$ for ET and $z\lesssim 1$ for CE) with a signal-to-noise ratio up to
several hundreds, irrespective of the detector design. When it comes to
parameter estimation, we use a Fisher-matrix analysis to assess the impact of
the design on the estimation of the intrinsic and extrinsic parameters. We find
that the CE detector, consisting of two distinct $L-$shape interferometers, has
better sky localization performance compared to ET in its triangular
configuration. We also find that the network is typically capable of measuring
the chirp mass, symmetric mass ratio and spins of the binary at order of
$10^{-5}$, $10^{-4}$ and $10^{-4}$ fractional error respectively. While the
fractional errors for the extrinsic parameters are of order $10^{-2}$ for the
sky localization, luminosity distance and inclination.
