People are more likely to enable notifications, location access, and the like on an app than a website; and an app doesn't need to be open for notifications to appear. You also get background update services for an app.
Drag and drop tends to work better in apps than mobile web (where the gesture often becomes confused with scrolling).
And on iOS at least, Apple's ecosystem provides some utilities that let you theoretically get away with not having a server (for purchases, game scores, and the like).
Have you considered a middle ground of something like react native?
1. If I need great graphics or better access to the phone's hardware, a native app is still your best bet. If you need better access to hardware, you may find some luck in the Phonegap/Cordova ecosystem but your mileage may vary.
2. If I had a key, extremely helpful investor who badly wanted an iPhone app in her portfolio, I would be very tempted to build one.
3. If my business model required an app, I would definitely build native. As an example, if my app relied on notifications, access to locations, etc I'd have more luck getting these permissions with an app.
Better UI than you can get via web (i.e. provide walking directions with a compass)
Anything that uses sound/music or highly responsive graphics like action games.