DirectX uses specific functions of the gpu.
Also minecraft is java if I'm not mistaken, not javascript.
It seems that using windows7 and chrome or IE provides the better performance with html5 games.
I'm using firefox on XP, and games aren't THAT fluid on it, but it's fine by me. (c2 runtimes seems to run better than HTML5 demos though)
Browsers will keep on evolving. Firefox has promised about a 40% improvement of its performance by march 2012 (even sooner). The browsers war still emulates improvement on their part.
So apart from changing your OS/gear, I'm not sure there's more to do but use chrome (best overall performances apparently) and wait for the browsers next updates.
It it a matter of time.