There are two question one in the title one in the opening sentence. Which is safer? Which is safer for an engine failure. Which one are you asking? the product marketing will of course say gyrocopter are safer then focus on engine failures.
It is probably a fair statement to say a Gyro is safer than say a R22 at entry following a engine failure.
It is also fair to say Gyros can have some interesting controllability issues that helicopters do not have.
A R22 can happily fly in 25kts of wind. From what I’ve seen AutoGyros can’t at least without pushing the limits.
A Jetranger or 350 are safer than both.
Autogyros have come a long way but it’s a long stretch to say they are safer than helicopters, engine failure is one of the least likely things to get you.