Well first of all when you run on a treadmill it will take longer to sweat because you probably don't have your treadmill outside under the sun. That is why you sweat more outside is because of all the heat. To answer your real question it really just depends how fast you are running. When you run on a treadmill it can only go so fast so your are limited to that speed. But outside you can run as fast as your body can handle. If you are running the same speed on the treadmill as outside you will probably lose more weight by being outside because you will be burning calories as well as losing water weight.