Anything I wouldn't be able to do by just going to the website? :/
The real advantage is for devs who can build an app that feels like a native app, but with one codebase for distribution across OSs/devices, not having to pay the apple/google tax, and not dealing with app review.
And you can put the PWAs in full sceen mode, whereas full-screen mode in a regular browser is almost always pointless ever since they took away tab indicators.