The Energon Pub

Is it possible to transfer users from one Xbox to another and keep online downloaded info?
I've been using my friends Xbox and made a user and even downloaded some stuff like for SF4 alternate costumes and such. And whenever I take the hard drive to a different Xbox it doesn't load any downloaded content. Well I recently bought my own Xbox and I'm curious if there's a way to maybe transfer users to my own and get that downloaded content again. Or would I just have to pay and download it again?
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If you have an Xbox live account, just log into your account on your new xbox. everything you've bought on that account will be downloadable (and you won't have to pay for it again), unless things have changed a lot since september...

I always wondered how to get saved games off it. In case you had to buy a new hard drive or for whatever the case.