Earlier quoted context omitted.
Actually, Firefox uses the platform decoders to decode patented codecs like H264 or AAC. So the operating system does play a role. I also think it's not unreasonable to believe that hardware accelerated H264 decoding works less well on Linux.
Good catch. So replacing "HTLM5" with "video codes", this may have a point. But I'm still wondering, as we have very good decoders from projects like FFmpeg and VLC. (Not sure which of all those decoders are used by Firefox.) These are platform independent and to my experience better than the platform specific libraries. For example, I often hear that people install VLC under Windows because it decodes lots of video…
Firefox does ship a lot of other video and audio codecs though, such as vorbis, opus, theora, vp8, and vp9. It's recommended to use these for HTML5 when possible because they can be easily supported everywhere.