First try physically swapping the HD's to see if either will startup on the other machine. I've had good experience moving Windows 7 HD's to other machines. It will swap out all the
drivers, request several restarts, then work fine if it starts in the first place.
Several have reported that they didn't even need to change activation, however I have always immediately changed out the key at Computer>Properties link to refresh it on the new hardware. If you needed to do more, you can run a
Repair Install which resets the activation and fully acclimates to the new hardware.
Before trying this, I would create a system image of each HD saved externally, so if necessary you can reimage it to the other machine's HD. You can even save the image in a primary partition on the same or secondary HD. The booted DVD or Repair CD will detect it there to reimage via network to other HD.