  A fundamental difference between a neutron star (NS) and a black hole (BH) is
the absence of a physical surface in the latter. For this reason, any remaining
kinetic energy of the matter accreting onto a BH is advected inside its event
horizon. In the case of an NS, on the contrary, accreting material is
decelerated on the NS surface, and its kinetic energy is eventually radiated
away. Copious soft photons produced by the NS surface will affect the
properties of the Comptonised component dominating spectra of X-ray binaries in
the hard state. Thus, parameters of the Comptonised spectra -- the electron
temperature $kT_{\rm e}$ and the Compton $y$-parameter, could serve as an
important tool for distinguishing BHs from NSs. In this paper, we
systematically analyse heretofore the largest sample of spectra from the BH and
NS X-ray binaries in the hard state for this purpose, using archival RXTE/PCA
and RXTE/HEXTE observations. We find that the BHs and NSs occupy distinctly
different regions in the $y-kT_{\rm e}$ plane with NSs being characterised by
systematically lower values of $y$-parameter and electron temperature. Due to
the shape of the boundary between BHs and NSs on the $y-kT_{\rm e}$ plane,
their one-dimensional $y$ and $kT_{\rm e}$ distributions have some overlap. A
cleaner one parameter diagnostic of the nature of the compact object in X-ray
binaries is provided by the Compton amplification factor $A$, with the boundary
between BHs and NSs lying at $A\approx 3.5-4$. This is by far the most
significant detection of the imprint of the event horizon on the X-ray spectra
for stable stellar-mass BHs.
