All multimedia content creation apps. Think DJ apps, music creation, audio editing, video editing, 3d modeling, image editing and illustration, etc. Basically everything that makes computers creative tools instead of information management devices. I don't see web versions of any of these seriously challenging native any time soon. Hell, even spreadsheets and word processors are still better in native.

I don't understand why this has to be an either-or thing. I know it's easier for us to think in black and white terms but I don't see why web and native can't coexist for a long time.

From your comment it becomes clear: At the moment "web" is primarily a data display platform. Not surprising, given its pedigree. Input techniques are quite limited... Especially responsive ones we've become used to on mobile. Sounds like a good project to work on..

Those are all desktop apps, though. Mobile apps - like the ones referred to by the article - are rarely for content creation.

Not yet, but these things are converging. There are already fledgling implementations of a lot of these tools available for iPads.