Asm.js isn't a solution for JavaScript developers, it provides an efficient compilation target for porting C/C++ code-bases to JS by leveraging Emscriptem or Mandreel compilers.
But this doesn't benefit the 99+% of websites running normal JavaScript. Whereas the goal of StrongMode is to carve out a safer and faster "subset" of JavaScript that's less error prone and easier to optimize with more predictable performance.
Only SoundScript is proposing adding (TypeScript-compatible) optional typing that's built into V8. ES6 is source compatible with TypeScript which can be transpiled to strip its type annotations so it runs in ES5 JS VMs. Essentially this is an evolutionary enhancement to JS.
That still wont be used by 99%+ of the websites out there.
At least not unless they want to forgo standards, or forgo strict-mode in all browsers but Chrome, and last but not least: they will have to update the code which is already there, and IE6 told us how that works in practice.
Let's not help Google forge the internet a new MSIE with Chrome.
"Q: How does SoundScript compare to asm.js? A: They have different goals: asm.js is a low-level language designed to be a compilation target for other (mostly low-level) languages. SoundScript is a user-facing type system for direct use of JavaScript as a high-level language. Both are complementary, both are useful, and V8 is committed to both."