Hydrodynamic simulations of the merger of stellar mass black hole - neutron star binaries (BH/NS) are compared with mergers of binary neutron stars (NS/NS). The simulations are Newtonian, but take into account the emission and backreaction of gravitational waves. The use of a physical nuclear equation of state allows us to include the effects of neutrino emission. For low neutron star to black hole mass ratios the neutron star transfers mass to the black hole during a few cycles of orbital

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... and subsequent widening before finally being disrupted, whereas for ratios near unity the neutron star is already distroyed during its first approach. A gas mass between about 0.3 and about 0.7 solar masses is left in an accretion torus around the black hole and radiates neutrinos at a luminosity of several 10^53 erg/s during an estimated accretion time scale of about 0.1 s. The emitted neutrinos and antineutrinos annihilate into electron-positron pairs with efficiencies of 1-3 rates of up to 2*10^52 erg/s, thus depositing an energy of up to 10^51 erg above the poles of the black hole in a region which contains less than 10^-5 solar masses of baryonic matter. This could allow for relativistic expansion with Lorentz factors around 100 and is sufficient to explain apparent burst luminosities of up to several 10^53 erg/s for burst durations of approximately 0.1-1 s, if the gamma emission is collimated in two moderately focussed jets in a fraction of about 1/100-1/10 of the sky.