I have had good luck with cross platform Java using SWT. This will give you a nice native-look on any OS, and there aren't a whole lot of problems out there that require any JNI code. With any luck, you should be able to distribute the exact same codebase to both targets, and it should just work.
Having said that, you should evaluate whether or not you really need the cross platform functionality. At the very least, it will require you to test the GUI layer of your app on each OS (testing layouts, presentation, etc). With a large app, this becomes cumbersome very quickly.
In either case, choosing a cross-platform language from the start will give you flexibility in the future. If you were to write native code from the start, it would be non-trivial to port the code to another platform. It would likely be accompanied by several bugs, and would also require a port of all the test code to the new platform. You would run into synchronization issues with any new features, bug fixes, etc. With Java, you can write JUnit tests which will run in both OS's, and any bugs or new features will be propogated to both versions automatically.
It really does depend on your specific application. If you are anticipating a user base on both OS's, then that should dictate your language choice.