If privacy is what you want, use Better Privacy addon for firefox, it will delete the LSO.
Or, you could just make a wrapper for each browser.
mv /usr/local/bin/firefox /usr/local/bin/_firefox vim /usr/local/bin/firefox # write your script chmod +x /usr/local/bin/firefox Create .lso/firefox,chromium,safari directories and make each wrapper just link the directory that is supposed to hold the LSOs to the directory of the concerned browser.
When firefox is launched it will set the global LSO directory to it's own LSO directory, so each browser will access its own cookies.