Hello,
Following PAM (http://service.sap.com/pam), Safari 7 is supported since NW Portal 7.30 SPS11. So you have to update your stack.
Firefox (extented support and rapid life cycle) seems to be not supported on Mavericks.
Another option with Safari is to emulate IE, see this thread: SAFARI Compatibility Internet Explorer: Apple Support Communities
Regards,
Nicolas