I just did this with my LE.
I wanted to move my F4 data from my 60Gb HDD to my 20Gb HDD. I put all the small F4 files onto a Memory unit from the 120Gb HDD using the 'move' option.
Then i put the 20Gb HDD in, moved the files from Memory unit to the 20Gb HDD.
Then i used the move function to transfer my User Profile, you can use "Recover Gamertag" if you like.
Then i went into the Download History and re-downloaded all the LE content and DLC packs to the 20Gb HDD.
If you got any cars in the garage that are on Disk 2, they will be lost upon the first bootup of F4 as Disk 2 isnt installed to the HDD until it loads the profile.
Maybe launching on another profile, then installing Disk 2 first can overcome the issue.
And thats it.