Alon Zakai[1] gave a good talk[2] on the current state of WebAssembly, particularly on the current state of performance
When this transition period goes away, LLVM should hopefully compile to WASM binary as a target. The current path described in the video of WASM -> C -> clang -> llvm -> native-binary is a temporary workaround afaik.
LLVM is one of the best toolchains for many languages.
They are completely different things.
LLVM as a toolchain provides backends for many target machines, so as a compiler author you can just emit LLVM IR and (mostly)automatically be able to compile for x86, arm, mips, etc... And they have a wasm backend too, so the technologies are complementary -- you can use LLVM to compile to wasm. LLVM will do a fair bit of optimization too. The intent with LLVM is not to provide a portable binary distribution format, but to allow different compiler frontends to all share the same compiler backend logic.
By contrast, with WASM the assumption is that by the time it gets to the browser the ahead-of-time compiler has already done a fair bit of optimization, so what a wasm compiler has to do is much simpler.
WASM is also designed for space efficiency, since the code will be shipped over the network, and safety -- LLVM has a C-like notion of undefined behavior (which the optimizer makes use of), but this would be wildly inappropriate for WASM due to security (and portability) concerns.