A big part of the advantage is more consistent adoption by browsers. All the major browsers have experimental WebAssembly support already, and Firefox and Chrome are already shipping it (although it's off by default). Firefox/SpiderMonkey and Edge/Chakra have AOT compilation for asm.js, but notably Chrome/V8 doesn't (although they did optimize its performance significantly). Asm.js also still hasn't become a formal spec, while WebAssembly is already very close.
> A big part of the advantage is more consistent adoption by browsers. […] Firefox/SpiderMonkey and Edge/Chakra have AOT compilation for asm.js, but notably Chrome/V8 doesn't
Not quite. SpiderMonkey has AOT compilation, whereas Chakra and V8 throw it at the JIT, though Chakra's compiler is specially optimised for asm.js AIUI.
Thing is, specific support for asm.js is unnecessary, a sufficiently good JIT is good enough. V8 hasn't implemented asm.js AOT because it doesn't need to. I assume the same would be true of WebAssembly.
V8 hasn't implemented asm.js AOT because the authors claim not to need to; but if you compare the performance of a Unity3D WebGL export vs FireFox the gap is very wide.
