Asm.js is not Javascript. It's native code!
It's not a VM bytecode. It's assembly language, and the target machine is your native CPU. It is sandboxed by the browser. It is present on any computer with a browser and Javascript, which is more computers than have a browser and Java plugin, or any other plugin for that matter. Asm.js is less mature that Java, but it will grow up. It is currently supported by more browsers than Java, so even if it's crappier right now, it will eventually surpass and replace Java in the browser.
If you are thinking that asm.js is Javascript or is interpreted, you're thinking about it wrong. Think about it this way: Take an arbitrary executable. If you dissassemble it, you have some sort of assembly code. There are several different assembly language syntaxes, but they're all basically the same. Asm.js is basically just another assembly language, with two key differences.
The first difference between asm.js and any other assembly languages is that the only existing asm.js assemblers happen to assemble executables that are sandboxed by your browser. You can't do syscalls to use sockets or files or the Windows registry. You can't fork() or run non-asm.js executables. Still, if you can live with the "syscalls" that the browser gives you, you can run native code in any browser. The browser is your operating system.
The second difference between asm.js and other assembly languages is the really clever part! It is not just assembly. It is both valid assembly language that can be assembled to native machine code and also valid Javascript that can be executed by a Javascript VM -- and both ways of looking at it are semantically equivalent!
It's like being able to write a novel where the text is both valid English and valid Spanish at the same time, and the plot is the same no matter which language you speak.
So I lied. It is Javascript. But you shouldn't think of it that way. You write Javascript. Your compiler writes assembly language. Asm.js is assembly. The Javascript aspect is just a clever backwards compatibility hack. It could have been specified to have a more traditional and readable assembly language syntax, but then you'd need plugins and nobody reads assembly anyway. As is, it's machine code that happens to be able to run on any Javascript VM. This means you can deploy native machine code to any browser without a plugin. In the event that your browser is old and doesn't contain an asm.js assembler, that's ok! Your unmodified native code will still run, albeit more slowly, in a plain old Javascript VM such as everybody has had for years. Except lynx users.
The browser as an operating system is currently worse than a Java runtime plugin in that the browser has less functionality. However, browsers are currently better in that they have more penetration and a higher velocity of improvement. Long term, the browser as a full-featured operating system makes more sense than as a mere scriptable document viewer slash plugin container.