I'm a big proponent of the mobile web but based on cross-talk on Google Plus, I've discovered I use native apps a lot more than I admit. That's largely because I prefer to app my way into content creation.
It's a lot less tedious saving an image to Flickr from the Flickr app (although sending by email works fine for me a lot of the time).
I use my Lumia and my iPod Touch to do more in less time than ever possible on my laptop. I reckon I'll be able to extend the laptop's useful life for an extra year because I don't carry it as much.
However, a lot of websites won't discard their ad-encrusted wrappers to to work smoothly on a smartphone or tablet. Like @jezlyn says, "If there are mobile websites that worked similarly to their corresponding mobile apps, I wouldn't mind using web apps more." (Cheryl was the inspiration for this post.)
Developers! Have a look at GetGlue and start revising your work.