I see no reason why it wouldn't catch up. What makes a good UI on a native app? Fast responses and clean animations? Fancy transparency and 3D effects, perhaps. There's no reason a web browser couldn't do these things. Web UIs may always be slower than native but with fast enough processors it will eventually reach a point where you just wont notice the difference.

Why do you think so?

There has been serious improvement in many areas of mobile web/browser support in the last 12 odd months; for what I've seen. Thanks to Android, Chrome, Firefox and Dolphin.