The solution to this issue would be - copy the cs6 library from C:\Program Files\Adobe\Adobe Encore CS6\Library and place it at another loacation and rename it.
Now uninstall the CS6 Content and reinstall the 5.1 FC using the disc or the downloded FC you have. In this way you will recover back your 5.1 FC and can also use the 6.0 FC by pointing Encore to its location. I tried it and this works
And this problem will no longer be faced once the downloadble version of CS6 FC will be available.
see thread -http://forums.adobe.com/thread/1002454?tstart=0
Let me clear up some points. I am installing Production Premium CS6 upgrade from DVDs not a download. I upgraded from PP CS5.5 Encore 5.1 (32x) which is still installed. I have been caught with unexpected results in the past so I always run an Acronis incremental backup between each non-reversable step then I can mount the backup drive image. In this case the backup drive images were run before I ran the install Encore functional content DVD shows Encore 5.1 llibrary folder intact and an empty library folder in Encore CS6. After running the install Encore functional content DVD the backup drive images shows the no library folder in Encore 5.1 and a filled library folder in Encore CS 6. To recover the Library for CS 5.1 is a copy and paste from CS6 library or change the path in Encore CS 5.5 Edit>Preferances>Media>Library Content to point to the Encore CS6 library (since the files are PSD and should be the same).