While native has had roughly seven years lead when it comes to providing quality online experience, web apps can beat native easily. And no it's not that web apps or web development or talent for mobile web development is limited or is the bottleneck.
The bottleneck is usually the vendors and support of standards in the existing breed of mobile browsers that destroy the web experience.
For example, Apple introduced this shitty non-standard swipe gesture feature on iPhone Safari/iOS7 that breaks so many things:
http://stackoverflow.com/questions/18889666/ios-7-is-there-a...
But I think this will change with more competition among tablets and mobiles. IMHO, it is normal for the web to catch up a little later; but when it does native will find it hard to breath.