More stuff the web can't do that native apps can do:
* Request stuff from arbitrary URLs without a CORS proxy
* Open TCP and UDP sockets
* Be in the play store/app store AS a web app (home screen installation isn't enough; people still search for your thing in the app store, so even if the other problems aren't issues for your app, you still have to wrap your web app in a dummy native framework and upload it if you want users to discover you)
* Scroll like a native app without Safari's stupid rubber band scrolling the entire app at very erratic times
* Barometric sensors
* Background geolocation, background anything really
* launchActivityForResult so you can work with other native goodies
* Intent resolution for native actions
* Geolocation when the user has inadvertently blanket-blocked Geolocation for all of Safari instead of per-webpage. Thankfully Chrome comes pre-approved on Android and you can't accidentally make this mistake as a user
* Face tracking and other OpenCV-based stuff (it's been done, but JS is still not fast enough on mobile to handle these jobs)
* Display long lists of styled content and scroll without stalling
Still though I think touch gestures is really the killer missing feature. There isn't any canonically-supported way to do things like a simple Android ViewPager or pinch-to-zoom. You end up implementing a bunch of spaghetti code to do these things even in the best frameworks (Meteor, Phonegap + Polymer, Angular et al.). And then you find out the way your spaghetti code reacts is a tad different from the way someone else's spaghetti code reacts to the same gestures. This stuff really needs to be standardized on a OS, browser, or at least JS-framework level.
* Request stuff from arbitrary URLs without a CORS proxy
* Open TCP and UDP sockets
* Be in the play store/app store AS a web app (home screen installation isn't enough; people still search for your thing in the app store, so even if the other problems aren't issues for your app, you still have to wrap your web app in a dummy native framework and upload it if you want users to discover you)
* Scroll like a native app without Safari's stupid rubber band scrolling the entire app at very erratic times
* Barometric sensors
* Background geolocation, background anything really
* launchActivityForResult so you can work with other native goodies
* Intent resolution for native actions
* Geolocation when the user has inadvertently blanket-blocked Geolocation for all of Safari instead of per-webpage. Thankfully Chrome comes pre-approved on Android and you can't accidentally make this mistake as a user
* Face tracking and other OpenCV-based stuff (it's been done, but JS is still not fast enough on mobile to handle these jobs)
* Display long lists of styled content and scroll without stalling
Still though I think touch gestures is really the killer missing feature. There isn't any canonically-supported way to do things like a simple Android ViewPager or pinch-to-zoom. You end up implementing a bunch of spaghetti code to do these things even in the best frameworks (Meteor, Phonegap + Polymer, Angular et al.). And then you find out the way your spaghetti code reacts is a tad different from the way someone else's spaghetti code reacts to the same gestures. This stuff really needs to be standardized on a OS, browser, or at least JS-framework level.