For those interested in changing from Mull (now discontinued) to Firefox or any of its derivatives (Fennec, IronFox…) there is this very handy tutorial to do so:
Just note that at the step to restore the backup in the new browser, you should set the correct app id.
The browser keeps a lot of sensitive information, so blindly backing it all up might be risky. On the other hand, completely opting out if this (very useful) feature isn’t very user friendly.