Obviously doing any physical exercise you should be safe about it (wear a helmet while biking, have a light and reflectors if you ride at night, etc., and of course be conscious of your surroundings), but running solely by itself can be detrimental to your health because of the force you put on your knees on impact running on paved surfaces.
Given the constraints of what we're given, biking is far better for your overall health than running.
Around here, biking is too damn dangerous. Narrow, twisty roads.
If you run on the balls of your feet, rather than heel-strike, the impact is greatly reduced.
Running isn't super bad for you. You need medium impact to build bone density, which is a major protective factor in old age.
Both of the sports will cause damage, as they are both straight line repetitive motion exercises. In either case you want to think of them as specific or specialized uses of your fitness, while creating proper base fitness like flexibility and muscular balance in the gym/yoga etc. would be your non-specific work.
Any time you go very specific you are going to find a weak link.
Why do people prefer to run for hours instead of a more intensive workout in a minutes?
Looking at the typical runners [0], why would you desire a physique like that?
[0] http://diaryofakalechic.files.wordpress.com/2011/08/marathon...
Note that sprinters as well as endurance runners have to lift some weight at one moment or another. When I run my first half-marathon I was surprised that my arms were more sore than my legs.
Any exercise is going to carry some risk of injury, it's up to you to learn how to mitigate it.
Not all risks are equal.