Interesting question !
Their only commonality is the fact they have a rotor rather than a fixed wing .
A gyroplane has less moving parts and cannot hover . Yes it can stop mid-air and will quite safely slowly descend vertically but must be returned to forward flight prior to landing . Are they safer than a helicopter when the engine goes quiet ? I would say marginally yes in that the gyro is already autorotating and therefore you remove the risk of messing up getting the collective down and entering an auto in your helicopter . Other than that their both going down and will require a short run on landing .
I've done many practice auto's in R22's and H300's and must say I find my M24 gyro easier to handle engine off and generally do most of my landings engine off to keep in practice should the day come when the Rotax goes silent on me.
BG .