Have rode one but not owned one. Know lots of folks that own.
"Are they safe?" What are we talking about here, a chopper versus a standard bike or bikes in general?
I have been riding for over 20 years, only put mine on the ground once thanks to a careless driver that decided that stopping on a corner of the highway for no reason would be fun. My leather kept me form any real damage and I was back up in a second...mostly so I could give them a piece of my mind. After that I rode/ride offensively and spend as much time looking in mirrors and watching eyes as I do watching the road. As a comparison, I have been in more car/truck accidents than bike accidents.
Now, standard versus chopper. Choppers are very hard to control at low speeds, say under 30mph. The long front end makes the balance all funny which makes it hard during turns. After 30mph they ride smooth as silk (Unless you have a hardtail) and are very easy to ride.
For those that have mentioned about the "Noise", not all bikes are loud nor do they have to be. But, most owners want them that way. All to many people do NOT watch out for bikes so by having loud pipes this helps the drivers of cars/trucks to know they are around. Most of the accidents involving bikes are from drivers of vehicles not looking twice, like you should anyways, before turning or changing lanes. Were talking about folks that ride by the rules, not speed freaks on bikes that will do any speed limit in the USA in first gear.