How much faster? About half the speed of C.
Now, nobody in their right mind is going to _write_ in asm.js. It's not very human readable, or writeable. You write your code in other languages and then it compiles to asm.js. Which means that you can write in anything which has a compiler that produces it (so far, just emscripten, which converts LLVM output), and get something which runs inside a browser, with no plugins. So far, only Firefox supports this level of optimisation, but I'm hopeful that Chrome will join it. And even if it doesn't, the code will _still run_ in Chrome. It just won't be as blindingly fast.
What makes this particularly exciting is that today Mozilla announced that, over the last four days, Epic ported the Unreal Engine to asm.js. Four days, to port over an amazing 3d engine, and have this running in your web page:
And, one assumes, they're still optimising. I doubt they'll ever make it quite as fast as C. But I'm sure they can get faster.
And then we have a standard way of getting real applications running on any computer that can run a browser, no matter what operating system it's running on. This really does feel like a step change to me.
Original post on Dreamwidth - there are comments there.