Mozilla OdinMonkey is used for asm.js, it's a seperate engine in Firefox (https://en.wikipedia.org/wiki/SpiderMonkey ). The general purpose JS engine is SpiderMonkey (TraceMonkey, JägerMonkey). So, Firefox already excutes asm.js faster than general purpose JavaScript due to an different faster implementation. And you can easily imagine that other vendors will follow them with WebAssembly.
Then the only way to get that extra speedup bonus is to compile Javascript to WebAssembly.
Well, let's hope Google realises that crawling web apps based on WebAssembly will consume a lot of CPU cycles and will decrease their rank or not index them at all. This will put an damper so that WebAssembly is only used for SaaS web apps compiled from native C++ and not for the vast amount of general purpose websites as a CEO technique to speed up the page load - which would be a real trojan horse, and dangerous for the web. Maybe I should add "patent pending", so that Microsoft, Adobe et all won't cripple the web.