For me the biggest difference is the ease of performing a longer workout. I've done multi-hour rides on my bike outdoors without a problem. 30 minutes the exercise bike inside is about enough for me. Boredom, poor-alignment (though I do have a $900 spin bike at home), whatever. I've made it as long as a single hour before, but that felt pretty lousy and wasn't much fun.
So, as far as fitness, I'd go outside whenever you've got the chance. You'll have more fun doing it. And that is what really makes a fitness plan stick. You can force yourself to exercise, or you can get exercise while you are having fun doing something that you love doing. Which do you think is going to work for you in the long run?
