The treeadmill will be more beneficial overall. Unless you are using one of the new stair machines that more resembles an escalator, you will not be getting the full benefits of stair climbing. The stairmaster often only targets the calves and glutes because of its limited range of movement. The treadmill will engage quads, calves, glutes, abs, back and arms. It will give the higher calorie burn in a shorter amount of time since it works so many muscle groups. If you feel jogging is not as challenging, try increasing your pace slightly, adding hills or setting the treadmill to a random setting, or incorporate sprints. These will all increase calorie burn and build strength and endurance.

I personally like the treadmill. I think it doen correctly the stair master can give you a better workout. For that you have to keep your hands off the hand rails. This requires quite a lot of balance specially when your are doing it fast.

I can do that at a good pace now, but since it tires my legs and interferes with my deadlifts and squats, I stick to the treadmill. Weight loss is not my primary goal anyways