They are good for different things, atm. Rust is focused on people writing new code for the Web, and does well there. C++ is focused on porting existing applications, which works well for things like Unity, Photoshop, Google Earth, etc.
The reverse cases are sadly not that great atm. If you have a Rust application that uses SDL2 and OpenGL, for example, porting it to the Web is not that easy (you either need to port those APIs to something else, or mix Rust and C to get Emscripten's SDL2 and OpenGL support). And if you want to write new C++ code just for the Web, current bindings solutions are not polished enough.
But hopefully all those things will keep improving!
True, but there is an unfortunate amount of bugs in that area. We (I'm an Emscripten dev) would like to look more into improving Rust's Emscripten support, but there have just been higher priority items for us (and I guess others) so far.
The reverse cases are sadly not that great atm. If you have a Rust application that uses SDL2 and OpenGL, for example, porting it to the Web is not that easy (you either need to port those APIs to something else, or mix Rust and C to get Emscripten's SDL2 and OpenGL support). And if you want to write new C++ code just for the Web, current bindings solutions are not polished enough.
But hopefully all those things will keep improving!