The best way is to use rsync, I've set it up so it doesn't copy unnecessary files, or at least ones I'm sure aren't needed.
Here is the rsync command Iused (adapt to your specific Thunderbird profile location):
rsync -hazv user@remotehost.com:/home/user/.thunderbird/sbrer.default/* /home/user/.thunderbird/4nyb0.default/ --exclude=global* --exclude=Cache --exclude=ImapMail --exclude=Mail
This is a great way to get your e-mail accounts going on a new c........