The only way that you can transfer stuff is that you can use a memory unit to transfer everything very slowly by continually swapping in-and-out the harddrives.

 

The memory unit goes below the DVD drive.

If you have some space and are willing to rip apart the drives (needs some fairly small torx drivers mind- smaller than the ones you would have used to open the 360 for DVD flashing) you can use sata though- 360 drives are standard laptop sata drives in a fancy case. You can then use the homebrew stuff like http://www.xbox-scene.com/xbox360-tools/Xplorer360.php to transfer data.

There are also kits to play around with 360 drives like the datel xsata that do run over USB.

 

I suspect edgedancer misread your post thinking that you had just got a say 120 gig drive where before you had a 20 gig and now wanted to have all the fun of 120 but with the data the 20 gig holds- this is the usual question we get asked/scenario we get posed around here when people speak about hard drives.

There is no out and out easy way though as MS have no real interest in allowing you to do this- easiest you will get is rigging both drives to the sata of your computer (or via something like the xport).

 

Right you are Fast6191.