The FF version isn't important.
What is is whether the version of the webbrowser control which is effectively IE supports the HTML audio as you can see http://msdn.microsoft.com/en-us/library/aa741313(v=VS.85).aspx the webbrowser control is a layer between the IE container app and the MSHTML engine. If the shdocvw.dll is a different version from what your Real Browser is seeing then that could be why there is a difference.
The current version on my machine for info is 6.1.7601.17514 (that's in System32) there are in fact 2 versions on the machine, but they are in the WinSXS caches/backup areas.
I have just tried on my machine vb.net winforms with webbrowser control and going to translate.google, and the little speaker works on .Net4
but does not on .Net3.5
despite the icon appearing, so there must be another wrapper around this in winforms which is breaking the functionality.
So the solution would be to switch to .net 4