The QR code is the exact same data, but in a QR code.  The primary goal was that you could use the paper backup as both a backup, and a means to transfer a wallet to your smartphone, just by scanning it (there are currently no Bitcoin apps that leverage my wallet format, but I'm getting help to work on one, now).  But it would also be useful if you have a webcam setup for scanning QR codes -- it'll pick up the exact same letters as shown on the page, and you can just copy the text into the "paper backup import" dialog.

For anyone in this thread who has no idea what I'm talking about, the paper backup looks like this: