  A kilonova signal is generally expected after a Black Hole - Neutron Star
merger. The strength of the signal is related to the equation of state of
neutron star matter and it increases with the stiffness of the latter. The
recent results obtained by NICER from the analyses of PSR J0740+6620 suggest a
rather stiff equation of state and the expected kilonova signal is therefore
strong, at least if the mass of the Black Hole does not exceed $\sim 10
\mathrm{\,M}_\odot$ and if the adimensional spin parameter is not too small and
the orbit is prograde. We compare the predictions obtained by considering
equations of state of neutron star matter satisfying the most recent
observations and assuming that only one family of compact stars exists with the
results predicted in the two-families scenario. In the latter a soft hadronic
equation of state produces very compact stellar objects while a rather stiff
quark matter equation of state produces massive strange quark stars, satisfying
NICER results. The expected kilonova signal in the two-families scenario is
very weak: in particular the Hadronic Star - Black Hole merger produces a much
weaker signal than in the one-family scenario because the hadronic equation of
state is very soft. Moreover, according to the only existing simulation, the
Strange Quark Star - Black Hole merger does not produce a kilonova signal
because the amount of mass ejected is negligible. These predictions will be
easily tested with the new generation of detectors if Black Holes with an
adimensional spin parameter $\chi_\mathrm{BH}\gtrsim 0.2$ or a mass $\mathrm
M_\mathrm{BH} \lesssim 4 \mathrm M_\odot$ can be present in the merger.
