Are these both the same model 360? Or by "new" do you mean the one with the built-in wireless and such? If they are both the same "older" style you should be able to just swap them over with no trouble. I've got 3 different consoles and I've swapped the drives around by mistake (because they all look alike) and they worked fine.
I'm kind of assuming you bought one of the newer style 360s because if the drive cases were the same you would've tried swapping them already, right?
