I think it's hard to make the claim that apps are more popular than websites on the iPhone. Unfortunately, it's hard to find data on overall mobile web traffic (or total web traffic in general), but over 60% of all web traffic from a mobile device comes from the iPhone. My guess, though, is that the number of websites visited since the iPhone's release hugely eclipses the number of apps downloaded.
And I'm not sure you can call the app store a monetization solution either, considering that >90% of all downloads are free apps.