Assuming Shumway makes no assumptions about the system such as
byte order, it should work on TenFourFox (but may be substantially
slower). However, getting it to a useful state is likely some time
off in the future.
I don't understand what you mean by functionally equivalent; the
video opens in a separate window now. The real solution is to embed
or connect an H.264 decoder into the browser itself. This is
possible, but non-trivial. It is not likely to happen for
TenFourFox 38 (IonPower is the highest priority).
Shumway (https://github.com/mozilla/shumway/) can be installed as an extension. It used to work (rudimentally; swf files only, no flash movies), but stopped working with TFF somewhere between version 0.8.75 and 0.10.xx. I never found it to be of much use and stopped following its development a while ago. v0.8x works very nicely with TFF 31 (and much faster than with TFF 24 or 29 so it's even usable on my Pismo), but as soon as you update the extension to a current version, it's broken.
I don't understand what you mean by functionally equivalent;
I mean so it starts playing the video when openH264 would,
rather than through menus. (And identifies itself to sites in the
same manner as it, too). If the video has to be in a window as at
present, rather than in the page, then that would be fine.