Best way to do it is to install it clean on the other computer. Your
current setup includes all drivers and configuration settings based on the
hardware setup for that specific computer. If you move the hard drive or
restore an image to the other computer , you will move all drivers and
settings as well.
You then have to backtrack, making sure you get rid of all the old driver,
change all the settings and if you have any issues, you'll be picking
through a needle in a haystack trying to source the problem and you'll never
be sure if it was because you simply moved the hard drive or restored the
image.
Install XP on the new system, when you activate, assuming it has been less
than 120 days since you activated XP on its present system, you will be
presented with a phone number to call in order activate on the new system.
Just tell them what you've done and they will give you a new activation
number, then install your apps, restore your data from backup and you're
good to go.
NOTE: even if you just moved the hard drive or restored an image, you would
run into an issue with activation as the setup would know it is not
activated on the new system as the hardware hash would not match.