I don't know if it's a PWA by some strict definition, but Fastmail has always been the best web app I've seen.

Looking at the replies to your comment, it appears there is a certain category of app that is better on the web (although it sounds like in many of those cases it is because their native app is so poorly implemented).

So, we're not likely to see video editing software on the web surpass native any time soon.

Tinder is a good example from a mainstream company. Also Facebook: better tha there mobile app.

Facebook is only better in the web in that it’s harder to track you. Uploading images, videos etc anything complex sucks.

I say this as someone who deleted the Facebook app and only uses web because of tracking.

I don't know about great, but using Twitter as PWA on the iPad was better than the app b/c the iPad app was so bad. The app has since gotten better though.

Little Alchemy 2 is a PWA and it’s been great since I installed it on my home screen.