I have read the doc on how to migrate to a new computer: Channels Support - How do I move Channels DVR Server to a new computer?
But I am also physically moving the hard drives that contain the Channels Database and config files to the new computer.
How does that change the restore option?
I would assume if the paths to the config (app directory) and recording directories are the same on the new computer, the only thing to consider would be change of IP address and needing to change port forwarding for remote access.
If the paths to the config (app directory) and/or recording directories changed, you need to restore from backup.
If you have any additional secondary storage paths or local content import paths defined, you should also check those after the move.
It doesn't hurt to restore from backup as long as the backup is current and you haven't done any new passes or recordings since the backup was done,