Regarding Firefox ... we experienced an bug with Firefox 35.0.0 with Kerberos auth and so I guess yes, it could be an issue maybe related to Firefox/Chrome.
Btw. The Kerberos issue was fixed in 35.0.1.
Beside some others seems also to have issues with PHP 5.6, so maybe (when you're at PHP 5.6) try to downgrade.
As a side note, we use auth ldap and auth pass thru and PHP 5.6 with all three browsers and everything is fine in our environment, so maybe it's something related to your environment - as a sysadmin I know that troubleshooting sometimes drive you nuts.