Could you expand on this? It seems like an apples and oranges comparison.

Asm.js only allows numeric operations on emulated heap buffer. You can do much better with OpenCL on CPU device.

Asm.js intended to be used as a backend for compilers. One of OpenCL use cases is the same.

Asm.js code pretends to be a JavaScript code, OpenCL does not, but there is WebCL - a JavaScript binding standard for OpenCL.

Asm.js is still JavaScript. You can do all kinds of things that JavaScript can't do by itself if you call native code with a plug in. That's the difference. No plugin. No installation.

What's the difference between Mozilla deciding to bundle Asm.js with Firefox vs. Google deciding to bundle WebCL and WebGL with Chrome?

I refer you to http://asmjs.org/faq.html to understand the difference. Particularly the Question: "Why not NaCl or PNaCl instead? Are you just being stubborn about JavaScript?"