On my workplace PC, I tried playing a video clip I uploaded of some goldfinches and noticed that Firefox could not play it properly in 1080p. The video was uploaded direct from my camera, so YouTube ended up using 50FPS which my camera records at and turned out to be too much for the 8-year old PC:
I then tried it in Chrome just to see how it fares. Not only did it play fine in 1080p, I brought up the stats and noticed that it's using the VP9 codec. From a quick search, it turns out YouTube announced a few months ago they're using VP9.
When I tried in Internet Explorer 11, I was surprised to see it also had no problem playing the video despite using the H264 codec:
So it looks like Firefox either does not do hardware acceleration in HTML5 video or is not efficient at it. This doesn't really surprise me with how much memory it keeps hogging lately after an hour or two of use. All three browsers played the video in HTML5, i.e. no Flash player.