James, I really can't say if it's bad for you or not. When I first started running it hurt my knees and my back very bad. Then I acclimated to it and my knees got better. Back improved from better lifting habits.
I don't run now, but did feel good when I was doing it. One physician who I know insists that running is actually good for the knees. Running, not jogging. Of course he's a runner so his opinion may be biased.
A big part of making my own running less painful and more productive was getting
running shoes that were specific to my feet. I probably tried on 30 pairs after they measured me at the shoe store and told me which ones to choose from.
The elliptical is likely to be much easier on the knees if they have problems though. No jarring and bouncing on them.