It depends on the context. If you move around before you are absolutely ready or willing, it can be very... depressing, but then again, it depends on you too.
I agree with Elena. And once you feel independent, it feels absolutely fulfilling to move around and explore your options. To me, I love it! It pretty much follows a similar pattern: At first you don't know anyone and try to fit in, with me it's always a bit delayed because I'm not too sociable at first, but once you find friends, it's a rush! Of course you miss your old friends but you wouldn't really go back to where you were just because of that. In my experience, every move is a challenge and teaches you new things. New cultures. New people. New experiences. It's awesome.
Now, my teenage years were pretty much the definition of emo. If I had had to do this moving around thing I do now back when I was a depressed teen, I would have hated it! It's all about timing! And personality. So... I guess in general it feels thrilling as long as you enjoy it but once in a while you feel this lack... you miss your parents, your friends, your cat, so it's timne for a visit. But the more fun you have at the new place, the less you feel alone and nostalgic. :)