In my limited experience I've ridden around 50,000 miles of street and maybe a 1,000 of dirt (all single track/gnarly trail/two-track combined). Learned on the street. I've done just fine on the street but crashed twice in the dirt, first crushing my foot, then a twist fracture in my leg (not fun).
So in my experience, the dirt is not as deadly, but definitely harder to learn and more chances of being maimed. A bad street accident is far worse, no question, but if you are a weekend rider, occasional tripper, then I'd say street is safer. This also assumes you aren't a fuckwad and have half a brain and leave your ego behind when riding street.
I'd agree with others that learning dirt makes you a better street rider, but that doesn't necessarily mean dirt is safer. YMMV and all that jazz. Also, telling a teenager you can't do something just makes them want to do it more