I'm gong to disagree here and say that heart rate does matter. It is the an indicator of how much blood your muscles are using, which is an indicator of the amount of oxygen being used for energy utilization (measuring VO2 from the lungs would be more correct). It will take much more time to burn the same amount of calories when the heart pumps at 70bpm compared to 140 and plus you won't be getting.
I do completely agree that the heart is not using much energy compared to the rest of the body.
As for the topic, I believe running outside is the best because you have to throw and then catch yourself during each step whereas on a treadmill you're more or less keeping pace. I like to do HIIT style workouts on the track because I can truly sprint a lot faster compared to the treadmill.
However, I gauge my workout by calories burned and not time or distance, so I end up using the treadmill the majority of the time.