I am speaking from the perspective of the safety of the aircraft itself...
Who is flying the aircraft can make a big difference in accident statistics. A dork of a pilot in a flight design is probably far more likely to have an accident or a fatal accident than a high-caliber pilot in a well-designed and built gyroplane.
But there is no getting around that on all gyroplanes, there is a slew of potential single points of failure that could lead to a crash and most like a fatal crash.... Rotorhead alone there is 4 individual bolts that if any single one of them fails, your dead. Almost all gyros, the control system.... If any single piece of the controls fail, you will have a total loss of control... And I have yet to fly a gyro that would be landable with a loss of controls. Gyros also have truly unknown lifespans for the airframe, the rotor, the rotor bearing, etc... Most people never fly them enough to wear any of these parts out, but do we really know how many hours the mast can last, especially on the euro style gyros where everything is harder and more brittle ( the metal used for construction ) and then all the parts are welded verses bolted together.
Compare that to the flight design, where the entire plane is really just 4 pieces.... with minimal points of failure. And most airplanes can be safely flown with just trim....
And you have the parachute when all else fails.
Enginewise, I would say anything powered with a Rotax four stroke is going to be equally reliable, no matter if it is a plane or gyro. But compare a gyro with a one of a kind converted car engine, to any other aircraft with a rotax 912.... You would be silly to think the car engine is going to be more reliable.
Does any of this mean gyros are deathtraps and you would be a fool to mess with one, NO. But to think that they are the safest aircraft in the sky, I don't think so. I think under some conditions the gyro is safer, ( like on a very gusty windy day ) And in the event of an engine failure, the gyro will be safely landable in a far tighter spot than most any other plane. Obviously a gyro can't stall or spin, so that is a positive thing... But you can find yourself behind the power curve which can lead to a accident if too low... And let's not overlook the fact that gyros do not tolerate Sustained zero G, and for sure any negative G... In alot of designs, Negative G will result in a PPO, but in ALL gyros, zero to negative G for just the shortest amount of time can result in the rotor slowing down to a point where they will not be able to sustain flight. In a plane you have to be aware to not stall, not spin..... In a gyro you have to be aware to not allow to be behind the powercurve too low and to stay positive G... Both aircraft have limitations