Depends on whether the new on has a serial drive and is set up with it, or has an original IDE. It will also mean reformating the drives and reinstalling OS/drivers and software, you cannot just swop drives and fire up again.
My 3200 64bit machine uses an IDE drive to boot and a serial drive as secondary.
Dispite what they say, this is the better combination.
If the new machine has a IDE drive and is set up, then you can add the old drive as secondary.
You can reconize the difference, the IDE drive has a large ribbon cable, either gray or pink, the serial drive uses a small brown ribbon cable.
You will also find that the old drive will have a much smaller capacity, possible less (unless it has been changed) than 80 gig, the new one will likely be 200 gig.