Firefox has had a GStreamer backend for decoding audio for a while now. This is quite handy since it enables supports for restricted codecs such as h.264, aac and mp3 which users otherwise need Adobe Flash for. Upstream is going this route already (https://bugzilla.mozilla.org/show_bug.cgi?id=794282).
Unfortunately the gstreamer support is not ready yet. Jan is tracking it.
The tracked bug is now fixed in Firefox 26, which is available in all Fedora releases.
I see '--disable-gstreamer' in about:buildconfig with 26.0 (3.fc20), no h.264 support in http://html5test.com/
xulrunner-27.0-1.fc20,firefox-27.0-1.fc20 has been submitted as an update for Fedora 20. https://admin.fedoraproject.org/updates/xulrunner-27.0-1.fc20,firefox-27.0-1.fc20
xulrunner-27.0-1.fc19,firefox-27.0-1.fc19 has been submitted as an update for Fedora 19. https://admin.fedoraproject.org/updates/xulrunner-27.0-1.fc19,firefox-27.0-1.fc19
xulrunner-27.0-1.fc20, firefox-27.0-1.fc20 has been pushed to the Fedora 20 stable repository. If problems still persist, please make note of it in this bug report.
xulrunner-27.0-1.fc19, firefox-27.0-1.fc19 has been pushed to the Fedora 19 stable repository. If problems still persist, please make note of it in this bug report.