This is like asking to prove the sky is blue in a sunny day. Walk outside and you'll see it. I was talking to friends about how we've forgotten how fast computers are because all we see are web pages and Electron applications. People don't even remember the wonder of native applications.

Try building an operating system or browser engine in Javascript and you'll see what the parent is saying. I'm just giving you these examples because these are some of the last remaining native applications everybody still uses, but pretty much any native application will be much faster than the Javascript version. The reason browser wins is that we got to a point where the performance is "good enough" and the development cost is significantly lower.