How does a brisk two-mile walk compare to a two-mile run on an elliptical machine? How effective is exercise on an elliptical machine as a weight-bearing workout?

A question to the Ask Well NYTimes columnist. My hospital did not have ellipticals and I absolutely hated treadmills. I could never get to any speed in walking, everything was wrong, push off, heel strike, dorsiflexion, knee flexion. On ellipticals at the gym I could not use the ones with the moving arms, the spasticity in my left bicep and pecs prevented any smooth extension of the arm, so I hung on for dear life to the fixed grips.
http://well.blogs.nytimes.com/2014/04/11/ask-well-elliptical-training/?_php=true&_type=blogs&_r=0
And with all the research that says exercise is great for your cognition and neurogenesis this would seem to be required for all therapy departments. But don't listen to me, I know nuthin'.