I put together a tutorial on how to create a famo.us (awesome framework for high-perf web apps) and use ManifoldJS to deploy it to several platforms. In this case, iOS.
It all comes down to what the developer for that app chooses to support. I'm sure there are a number of native applications, regardless of the platform, which look or perform poorly as well.
For a web app to really stand out from the web site it is coming from, it should offer some sort of benefit to the end user that could not be found on the site itself.
Discolsure: I work at Microsoft
Assasin's Creed Pirates (iOS, Android) is a BabylonJS (WebGL) game wrapped web app (not with Manifold) and deployed to the app stores. Great views, gorgeous visuals.
So a web app can be a lot more than just a wrapped, simple app.
You can always go in and edit the Cordova project that ManifoldJS returns and add your own images for icons and such. Not sure if ManifoldJS currently supports this out of the box just yet, though.
Good use of a data set and illustrates what's possible.