You can do either one- I had traded in my old copy of DA, so I picked up the retail disc and play if off there. I still have all my old saves on my HDD, though, so my character and my old plot stuff is still there, though- it was pretty sweet in Awakening when Alistair showed up all stately as King and actually acted like a bad-ass monarch instead of a whimpering little pussy like in the original. Kind of like he had learned how to command some respect for a change. Of course, given that there are multiple ways for the "who rules the kingdom issue" to play out in the first one, it would be pretty interesting to see how those scenes play out if he's not in charge, I would think.
Oh, yeah, back on topic, though- you can just DL the content if you want, then you have to have your old original disc in the tray to play and it treats it like The Stone Prisoner or something like that, basically. It's huge, though, I think 1.8 gigs, so even if you have the original, buying the disc will save you a nice chunk of HDD space.
Yeah, I remember when you figured that out on Shivering Isles- I actually looked for a copy of GotY edition at my local BB Video, was going to try the same thing, but of course, shitty ghetto BB that it is (they carry jack and shit for games), they had no Oblivion of any kind, GotY or otherwise. So I just ended up buying a used copy of GotY for $22.50 since I didn't have any Oblivion at all at that point.