Elliptical machines are easier on your body. However, Jogging is a lot more efficient, because it isn't easier on your body. When you bear weight while running, you're also strengthening your bones and more muscles throughout your body (which, of course, costs calories to repair). You just don't get that while on a treadmill or elliptical.
If you have to do elliptical though, I think as long as your heart rate is elevated for an extended period of time, you should be good. It isn't as great as running, but few things are.
