OK, so as engines don't quit (as least not in single engine helicopters, they do, as anecdotal evidence has it, quit occasionally in twins, and that should be a non-event, but people do struggle) it kind of doesn't make sense to compare the safety of two different aircraft classes solely based on the simplicity of their engine off emergency procedure.
Rotorcraft accident happen, caused by a variety of reasons: energy mismanagement, CFIT, pilot induced oscillation, neg G, significant turbulence, mismanagement of rotor RPM, over-control, spatial disorientation, mid-airs, rotor strike, tail rotor strike. Some of these cases apply more to gyros than to choppers, some the other way round (TR strike in gyro is not that common).
I hold (or held) licenses for both aircraft. Still I don't consider myself expert enough to answer your question. However, I see gyros mostly being operated during the hour of calm air, mornings and before sunset. That might tell you something.