Similar questions to this are asked periodically, but many of these answers are outdated.
I need to build a cross-platform desktop application in Java with a GUI of comp
Have you looked into JavaFX 2.0? It is designed to interop easily with Swing, and has many modern 'good looking' controls.
Also, as lrAndroid mentions, a Swing app can look like a native app if you set the system look and feel with:
UIManager.setLookAndFeel(UIManager.getSystemLookAndFeelClassName());