We present the first direct comparison of numerical simulations of neutron
star-black hole and black hole-black hole mergers in full general relativity.
We focus on a configuration with non spinning objects and within the most
likely range of mass ratio for neutron star-black hole systems (q=6). In this
region of the parameter space, the neutron star is not tidally disrupted prior
to merger, and we show that the two types of mergers appear remarkably similar.
The effect of the presence of a neutron star on the gravitational wave signal
is not only undetectable by the next generation of gravitational wave
detectors, but also too small to be measured in the numerical simulations: even
the plunge, merger and ringdown signals appear in perfect agreement for both
types of binaries. The characteristics of the post-merger remnants are equally
similar, with the masses of the final black holes agreeing within dM< 5
10^{-4}M_BH and their spins within da< 10^{-3}M_BH. The rate of periastron
advance in the mixed binary agrees with previously published binary black hole
results, and we use the inspiral waveforms to place constraints on the accuracy
of our numerical simulations independent of algorithmic choices made for each
type of binary. Overall, our results indicate that non-disrupting neutron
star-black hole mergers are exceptionally well modeled by black hole-black hole
mergers, and that given the absence of mass ejection, accretion disk formation,
or differences in the gravitational wave signals, only electromagnetic
precursors could prove the presence of a neutron star in low-spin systems of
total mass ~10Msun, at least until the advent of gravitational wave detectors
with a sensitivity comparable to that of the proposed Einstein Telescope.
