The 360 HDD has a virtual Xbox hard drive partitioned into it with a C:, E:, X;, Y:, and Z: for emulating Xbox games. The only way to get this on the HDD is to either have the one that comes with the premium OR buy the one off the shelf.
The external HDD will act like a storage device...music, video, pictures and the like...but will not function like the 360's.