GStreamer 1.0 has been out since September of 2012 and with many changes. The upstream GStreamer 1.x development meanwhile is up to GStreamer 1.4 and now only with Firefox 30 is the new API being supported. Up to now, Firefox has still been relying upon GStreamer 0.10.
GStreamer 1.0 support for Firefox has had an open tracking bug going back to October of 2012. There were work-in-progress patches for porting to the new multimedia API throughout 2013, but only with this next Firefox release will Linux users be able to use the latest GStreamer. The only downside of the Firefox code in its current state is it appears the GStreamer 0.10 code-paths are the default but at build-time it needs to be configured with --enable-gstreamer=1.0. Sadly it appears there's no dynamic detection support and Mozilla developers are being conservative with Debian stable not having GStreamer 1.x packaged.
Firefox 30 also has a new Box Model Highlighter, new CSS property support, ECMAScript 6.0 support improvements, and many other changes. While Firefox 30 is now in a beta state, it will be officially released in June. Details on the developer changes for Mozilla Firefox 30 can be found via the Mozilla Developer Network.