TL;DR:
The sound to me is a loud hard disk searching around like crazy on disk.
If I'm right, the Kinectless and Kinect-models should have different harddisk revisions or even types.
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Explanation:
Tinfoil hat time!!
Well, consider the following: When you let a Windows machine idle, it sits completely idle for some time, doing nothing. If you don't do anything, very often a background process is started to do something, which usually uses lots of random disk IO. MS has been doing this for a long time.
When your game is idling in the menu it usually does not have lots of random IO, but rather reads large chunks at the same time, which is quiet.
So, what could cause random IO, when idling your xbox? Windows examples from the past:
1.) precompiling .NET byte-code
2.) a nasty hd indexer
3.) the windows update service looking which updates are installed and which updates need to be installed.
4.) background defrag
Something like 3.) is the most probable use-case for the xbox in my opinion. The Xbox advertises stuff for you to do on the dashboard and these things are targeted as far as I know. (I just remember a controversy about targeted political ads; don't know how it went in the end.
http://www.gamespot.com/articles/mi...ashboard-courting-conservatives/1100-6418181/ )
For that it needs to know, what is installed and what is not installed. Usually this should only be a list, but the same things applies for Windows Updates.
This doesn't explain why the kinect-model doesn't do it. Well, many different harddisk models get louder after usage especially during random access. So MS could be using a different model in the Kinect-less and Kinect models. I would like to tell you to pry open your boxes, void the warranty and prove me wrong, but I guess it's better if you don't.