It seems to me that RoboVM+libgdx is utilized heavily for the game industry. Correct me if I'm wrong, most games don't use UI components (most of the time it's a full-screen game) the way regular apps do so I'm wondering if RoboVM is a good fit for Rich-UI mobile apps?
That's correct, most games will never touch the native APIs, except for things like IAP or Facebook/Game Center/Google Play Games Service integration.
RoboVM gives you full access to all iOS native APIs in idiomatic Java. Have a look at the Javadocs [1] to get a feel for how that looks like. Currently not wired up to the Apple docs, but that's on our roadmap. We have quite a few ports of official Apple demo apps [2], a simple hello world looks like this [3].
You can even extend ObjC classes as if they were Java classes and/or implement Protocols. Binding of native APIs (C, ObjC) is accomplished via something called Bro, which is annotation-based and a lot simpler and faster than using JNI.
So, yes, i think RoboVM is a good fit for Rich-UI mobile apps. Performance is great (we use LLVM), and the bindings are pretty complete. We currently lack interface builder integration, but that's on the short term road map (and for anything other than a quick prototype you don't use IB anyways).