The problem is that one xbox has a game update and the other one doesn't.
What you need to do is clear the cache on both xbox 360's so they don't have any game updates on them.
This is about the same but the instructions are for the older dash but once you go to the memory option then it's the same code.
To clear the cache on the Xbox 360 do the following:
* Go to the Xbox Dashboard, select the System Blade, and select Memory.
* Highlight the HD symbol and press Y.
* Press X, X, Left Bumper, Right Bumper, X, X