It depends on the speed and the treadmill. The biggest difference is lack of air resistance on the treadmill. As speed increases, the wind resistance increases. In the study above, slow speeds (about 6-7 MPH) corresponded to a 0-1 degree incline while the faster speeds (about 9- 11 MPH) corresponded to a 1-2 degree incline.
This doesn't mean that you should run on a treadmill at 1 degree incline all the time. The goal isn't to obtain the same energetic cost. Some variety is good.
Walking up a steep incline isn't all that similar to running. Actually, in a lot of ways it's more similar to biking.