hi samk,
i donĀ“t know the exact behavior of the different browsers in all technical details,
but nevertheless i want to give you some hints:
minefield is collecting far less protocolls, journals and logfiles compared to firefox.
icecat works in a resembling way and gnu and fsf are looking for some security concerns, too.
if security and value of personal data is a central topic for you,
i suggest to use icecat, together with noscript and https-everywhere.
the next step could be to start every session with a lean basic set of config-files in your browser-configuration or just delete all *.sqlite-files at every reboot.
there is some extra work to do, f.e. if you change some options or preferences, but you enhance you privacy in many ways.
on the other hand by using always the same set of lean-config-files you reduce the size of your backup-file.
mine f.e. is far smaller than 2mb and it includes many configuration files, scripts, binaries and even some funny stuff, too.
i hope i could give you some interesting hints.