Try clearing the hard drive cache..
To perform the function, access 'memory' in the system blade, and then highlight the hard drive. Now press: Y, X, X, LB, RB, X, X. The following message should appear: "Do you want to perform maintenance on your Xbox 360 storage devices?"
You will then need to connect to Live and place the original Xbox 1 disc in the system.
It should redownload the update.
The reason it works on one hard drive and not the other is because the software is installed on the HD. one has it and one doesnt.