Running on a treadmill is physically different from running on solid ground, and therefore it doesn't feel exactly the same to your body and often feels harder at first, much like the difference between riding a real bicycle vs. an exercise bike. My suspicion is you're trying to run too fast outside. Just slow down a bit, don't worry about not having that nice electronic display in front of you to tell you how fast you're running or how far.
Once you get used to running outside, I would bet dollars to donuts you'll like it it better. I find running on a treadmill to be more difficult now that I've been running for a couple years. I hate them but they're sometimes necessary if it's snowy or too cold outside where I live.