FWIW the native and WASM versions of my home computer emulators are within about 5% of each other (on an ARM Mac), e.g. more or less 'measuring noise':
https://floooh.github.io/tiny8bit/
You can squeeze out a bit more by building with -march=native, but then there's no reason that a WASM engine couldn't do the same.
SIMD and multithreading support really helped with closing the performance gap.
Still surprised about the 5% though- I’ve generally seen quite a bit more of a gap.