I started on the treadmill, and think it's good if running is not something you've ever done much of. You can start off slowly (I walked on it for the first two weeks), and there are fewer things to worry about (cars, dogpoo, uneven surfaces, darkness, weather, being far from home, and just the unstructured style that outdoor running brings). There are also usually qualified people there to help you out, there are other fit/sexy people to look at and get motivated by, and there are usually TV's or entertainment, so you can distract yourself whilst your body builds up a tolerance.
Having said all that, I agree with the majority of replies - being outside is great. Despite being a 45-minuter on the treadmill, I did have to start again when I went outdoors, getting used to all the elements mentioned above, aswell as the local pikeys watching me as they lurked outside Mothercare. But I did get used to it, and am now running 1hr20 outside, and did my first 10k race on Sunday.
If you like gadgets and you've got some spare cash, try a Garmin Forerunner 201 - it tells you your speed, distance and time, so it's a bit like you're on a huge world-sized treadmill. Which of course we are.
And the best advice has already been given - do what makes you happiest.