Native views and web views are good at different things.
Native is good for high fidelity interaction, animations, responding to gestures. However the native APIs are bad for designing "documents" -- that is, layouts where elements flow within a container and push each other around. That means that things that are extremely easy on the web can be painstaking in native UI without much upside.
Web views have limited interactivity, but they have other advantages:
* Faster iterations. You don't need to push a build when a webview changes.
* Document-style layout, as mentioned above.
* Higher density. We found it easier to show more information on the screen with HTML/CSS than the native controls. Looking at other apps out there makes me think it's an attribute of the medium, not just us.
* No need to sync data or duplicate logic. Sending HTML down the pipe is simple.
Finally yes, we get the multi-platform advantages because the web views are also served to people who hit the regular mobile web version of the app without any wrapper.
I'm on a project where we're taking the hybrid approach and I can second all the points Ryan has made here. We are launching our app soon on iOS and Android so we're getting the full benefit of cross-platform compatibility. We've run into literally zero cross-platform browser issues during the process, too. Hybrid is definitely the way to go if your app is text heavy like Basecamp and our app.