I'm not a runner but I am a weightlifter and it stands to reason that outdoor running is better for you overall than the treadmill in the same way that freeweights are better than mechanical / pulley systems.
On the street you would be requiring more finesse from your limbs just by navigating the various ground conditions; stepping over curbs, going around slow people, leaping over dog poop
You would be sending more blood flow to the smaller stabilizer muscles in your legs. Whether it makes a cardiovascular difference, I don't know, but it makes an overall fitness difference for sure.
The only times I would take indoor over outdoor exercise are a) in the winter when weather and the risk of injury is much higher or b) in the summer when air quality can get pretty bad. In those instances you're better off in the gym.
For those of you who run - did any of you get shin pain when starting out and how do you overcome that?