Firefox supports 60fps if the video is encoded in WebM (VP9) which only happens on Youtube if it has enough views
Google could have added support in the Flash player
I get 60fps on test videos with single-digit views, using RHEL 6.4, Firefox 17.0.7 ESR and Flash 11,2,202,327.
Although the video options only present e.g. 720p rather than 720p60, selecting 720p gives 60fps. Selecting 480p gives 30fps. The same video encoded at 30fps before upload and viewed in 720p shows the difference very clearly. I suspect it's something to do with the old version of Flash.
For reference, I also tested with Windows 7, Firefox 33.0.2, Flash 184.108.40.206, and 720p and only get 30fps.