There's a ton of features in the native app that aren't in the webapp simply because web APIs a much more limited. I should probably list them someday.

Also, there's a few bugs with PWAs that can't be easily solved, but don't exist in the native app.

In my experience the App Store version is better

I started off using the web app but found after reading web links that the screen would blank out and I’d have to restart. (iOS, not sure if that matters). Have had no issues with the App Store version.

In Android (not sure about iOS), but PWA's history shows in the browser, which is a main reason of why I switched to the app store.

Not sure if it makes a performance difference, but the native version has app icons to switch, haptics inside the app, and you can tap the status bar to scroll to the top. There’s also a watch app. Don’t know if there are other differences.

Maybe the TestFlight version is more recent.