As lugg said, it took a long time for web apps to rival native apps in functionality, and there are still a lot of places where they don't (large files, graphics, etc). In ~3-5 years the class of web apps that are lightning fast on desktop now will be fast on mobile.
>and there are still a lot of places where they don't
This would be better phrased as "and there are still only a few places where they do". Google Docs, for example, is great for basic collaborative editing (as long as you don't mind the NSA reading it), but has a UI that it a total pain (especially the world's worst keyboard shortcuts, e.g. having ctrl-enter and shift-enter reversed, and completely lacks advanced features.
