I think 'feel fully native' is a misnomer. They are fully native. When you build for iOS you use xib or storyboard for layout (or native code adding views/subviews directly) and the same for Android, you use layout files.
There are lots of great apps out there, Rdio was one of the more prominent early ones and it is also interesting to note that Unity3D games run on the same underlying framework (mono) http://unity3d.com/showcase/gallery