Assuming the helicopter is mechanically sound, I'd consider a helicopter safer than a plane because it can do something called an autorotational landing. All the pilot needs is a relatively flat space big enough for the helicopter to land on to perform this maneuver. While a plane that looses power needs to find an appropriate runway.
It will vary from helicopter to helicopter, but there is a curve created by plotting foward speed vs altitude. Below this curve an autorotational landing isn't possible, above it, an autorotational landing is possible.
Here's some helicopter basics I learned from an Apache Longbow game manual
If we have any helicopter pilots here, feel free to correct any misconceptions or erronious assumptions I'm making from this most authorative source :p)
Helicopter controls:
Collective - 1 axis joystick that collectively controls the pitch on all the blades. Increasing the collective will make the helicopter go up, decreasing it will make the helicopter go down.
Cyclic - 2 axis joystick that cyclically changes the pitch on the blades at a particular point. Which ever direction you push this control, that segment of the blades will have their pitch reduced, and the opposite side will have their pitch increased. This will cause the helicopter to tilt and move in that direction.
Tail rotor pedals - two pedals that control the pitch of the tail rotor.
Throttle
What makes a helicopter so challenging to fly is that a change to any one of the above controls requires the pilot to compensate on the other 3. If you increase the collective, that will increase the resistance on the blades so you'll have to increase the throttle to keep blade speed up. These two will inturn create more torque so you'll have to compensate with the tail rotor pedals to keep the helicopter straight. And you'll likely have to slightly tweak the cyclic control as well.
Anyways, purpose of these descriptions was to describe an autorotational landing.
If the helicopter looses power and is above the autorotational landing curve the pilot will drop the collective all the way to maintain blade speed. He will then use the cyclic to maneuver the helicopter to the best landing spot he can find. Then just before the helicopter is about to hit the ground he will pull the collective all the way up and the cyclic all the way back. This will kill almost all down/forward momentum and result in a relatively mild drop the last few feet to the ground that will result in no damage to the helicopter. The further you go below the autorotational landing curve the more damage will occur to the helicopter and the more likely passenger injury will be.
You have to successfully complete an autorotational landing to get your helicopters pilots liscense.
