Moving my Firefox 'identity' to a newer install.

I've backed up my home directory, and installed a newer version of Slackware. Instead of keeping all my dot-directories I wanted to cherry-pick just the stuff for Firefox (to include bookmarks, history, passwords etc...). I started with ~/.mozilla/firefox and thought that should be all I'd need, but I ended up copying ~/.config ~/.cache ~/web_auto before Firefox would recognise my profile and load properly. I just wondered if it's explained somewhere what these things mean, and how I can copy just what I need. Unfortunately I don't remember which version of Firefox I've moved from.

Thanks!

PS: I'm using KDE.