The machine that raises your heart rate highest is the one that burns the most calories.
The number of calories burned during
any exercise is determined by your heart rate. So if your HR is 150 on the Stairmaster and 150 on the elliptical, then you're burning the same number of calories on both. Ignore what the machine readouts say, they're usually wildly incorrect. It's the same with any other piece of equipment -- at the same HR, you're burning the same number of calories. 150 on the treadmill = 150 on a bike = 150 doing step aerobics = 150 swimming. All of those activities would burn exactly the same number of calories because your HR is the same on all of them.
It's helpful to invest in a heart rate monitor. It constantly monitors your HR and gives you a more accurate number of calories burned than a machine readout does. And with a HR monitor, you can see that HR determines calories rather than the type of exercise. A HR monitor doesn't care what exercise you're doing -- all it cares about is your HR and it tells you the number of calories burned based on that number.
By the way, by wearing my HR monitor while I lifted weights, I discovered that weights can also be interval cardio!! I can get my HR up as high for a set of weights as I can on the elliptical.
Bottom line: if your HR is higher on the elliptical, you're burning more calories on it. On the other hand, if it's higher on the Stairmaster, then that's burning more calories. It's all about your HR.