Two completely different machines and your going to get both sides of the arguments. Both have their advantages and disadvantages so its whatever your most comfortable with. A lot of people with injuries love ellipticals because they limit the impact on their joints and if they have handles you can get a full body workout as compared to a stair stepper.

The elliptical will be easier on your ligaments/joints but I would suggest spending the extra money and getting a good brand such as Precor or some other commercial gym elliptical. With ellipticals I have found that you get what you pay for most of the time. Most of them have every feature you could possibly need including the heart rate handles and you can get incline versions as which can help mimick the stepper.