The major difference between outdoor and treadmill running is air resistance, but even discounting air resistance, you are likely to expend less energy on the treadmill.
One reason is that with certain running styles, the treadmill may overread. As your feet leave the treadmill surface, the belt will tend to speed up. If your running style is especially bounding, this transient speeding-up may become significant. Ah, I see that the PPOnline link provided by Finagle already makes this point, and others relating to changes in running biomechanics on the treadmill vs. Great Outdoors.