Zig can (eventually) do better than Rust because it includes the ability to compile C/C++ code to WASM, Rust needs an external C/C++ compiler for this (so you're back to having to deal with Emscripten if you need to embed C/C++ libraries in your Rust project).
The same is true in reverse, though, you need an external Rust compiler if you include Rust code in your C++ project. Mixing compilers and languages will always cause conflicts, I don't think either Emscripten or Zig will be any different other than that Zig has some backwards compatibility with C/C++.
