I also consistantly run faster outside than on a treadmill. I don't really know the exact reason. It could be that the treadmill you ran on wasn't calibrated correctly, so the pace or distance reading could have been off. There's also the mental aspect of running in place on a treadmill with little/no air flow. I can't stand it.
When I have to run on a treadmill, I now wear a heart rate monitor and just run for a certain time period at a specific target heart rate and totally ignore the distance and pace.