Don't look at asm.js benchmarks if you're interested in real-world JS. Look at them if you want to know something about the performance of C++ code transpiled to run in a browser, which is an interesting thing to know. And it's getting to be more and more relevant these days. (Even "real-world JS" is going to start using asm.js libraries, I bet.)
But asm.js execution is very different from JS execution, even in browsers that don't have specialized asm.js paths. Executing regular JS is all about balancing compile time and garbage collection with code execution. asm.js barely uses GC, and allows lots of opportunities to cache compilation in ways that would be invalid for regular JS. So the whole space of tradeoffs is different.
But asm.js execution is very different from JS execution, even in browsers that don't have specialized asm.js paths. Executing regular JS is all about balancing compile time and garbage collection with code execution. asm.js barely uses GC, and allows lots of opportunities to cache compilation in ways that would be invalid for regular JS. So the whole space of tradeoffs is different.