https://bugzilla.mozilla.org/show_bug.cgi?id=840282 has some measurements on how fast the implementation of asm.js (called OdinMonkey) already is.
"sm" is SpiderMonkey, that is the normal JS engine. v8 is Chrome's JavaScript engine.
Current results on large Emscripten codebases are as follows, reported as factor slowdown compared to gcc -O2 (so 1.0 would mean "same speed")
odin (now) odin (next) sm v8
skinning 2.80 2.46 12.90 59.35
zlib 2.02 1.61 5.15 5.95
bullet 2.16 1.79 12.31 9.30