I've used rsync again for this because I found it very simple, I've only excluded the Cache directory since it's not necessary and could be several GB in size.
rsync -Phaz --exclude=Cache/* user@remotehost.com:/home/user/.mozilla/firefox/profile.default/* /home/user/.mozilla/firefox/ec1n9opl.default/
This is a great way once again to get going how you were on the old/remote computer fairly quickly. It even restores all of your history including the very tabs that were open and also includes your bookmarks, settings and addons too!