The web has a long time to catch up in terms of technology (iOS has poor support for APIs that would make web apps compete with native) and culture (most businesses don't care that their app is slow and bloated and defer resources to the app).
I'd say the one really important thing web is missing is notifications for when your not on the site. I don't really know how a browser could ever implement in a similar fashion.
Email, or SMS? Though I don't see why Apples Push Notification Service, can't be opened up for the web side. They are already going through Apple servers correct? Safari has push notifications, let's combine the two.
