A:  Cardio-vascularly running outside and running on a treadmill are the same. You can elevate your heart rate to your aerobic threshold and can become aerobically fit doing either.

Believe it or not, running on a treadmill is comparatively passive exercise - what you are trying to do is simply keep up with the treadmill belt. When you are running outside, you have to propel yourself, therefore requiring more muscular activity ie. quads, gluts, calves. So running outside is much more active and will make you stronger and fitter faster.

Both are good for you, though!

Trainernyc