| Ah, the mother/child relationship. My mom has also got to be doing more/better/harder than me, too. I bet you didn't even know you were competing with her until she brought it up. ; )
ok, If you run on a track you get the added workout of air/wind resistance. At slow rates of speed this isn't much of an additional workout at all, but if you are hauling it could have a palpable effect.
But to be really honest, I would guess that any overall difference between the track and a treadmill is negliable, unless the treadmill is set on an incline, or unless you are running at difference rates of speed, intensities and/or distances, and really , it depends on your goals. If she is running to gain speed, but you are running to lose weight, you are both doing completely different workouts.
My recommendation is to sign up for a local 5k (make sure you get chipped timed so the winner will have proof to show at every family gathering for the rest of your lives). : D | 
