AFAICT, Browsix is meant to work more like Wine than like jslinux. The goal is to allow devs to deploy native executables to the web browser more seamlessly because it provides ways for standard javascript to interact with the program. JSLinux is a full system emulator and thus has more overhead and doesn't have a method to cleanly interact with the world outside of the emulator.
The latex editor example is the one that best demonstrates the concept. It is a standard JS frontend that is invoking an unmodified pdflatex for rendering. In all other 'OS in the Browser' projects I'm aware of it would have to be a desktop application that just happens to be getting rendered in the browser. With plain emscripten or webassembly you would need to modify pdflatex to support a method to accept jobs and return results while not relying on any OS level features.
For sure, it's amazing to get a full kernel running; there's so much one could do. But an emulator and a full kernel is going to have a sizable footprint, be a significant amount to download, and performance is going to be mediocre. Yes there's a linux kernel running, but it's inside a virtualization layer; if you want to integrate & have the page interact with the kernel, you'd need to start hacking some pretty wild channels to punch through that virtualization layer.
Writing an operating system that directly targets the browser, that offers the expected/standard system calls ought to be smaller and faster, and more interestingly, it can potentially integrate with the rest of the page in interesting fashions, easily.
It's about building the UNIX abstractions using web primitives, like WebWorkers and transportable WHATWG Streams. Very cool stuff. I've seen a lot of these here and this one is not underwhelming to me at least- if anything it is inspiring for how one might architect an advanced resource intensive client-side web app.