You should look at JavaFX. I just finished an app based on it. It's the official replacement for Swing and is quite WPF like in nature (scene graph oriented, etc).
Although there are skins that can make it look native on each platform, I didn't bother with this for my app. Trying to match native on a cross platform app is a fools errand. A few months after you ship your app, the OS developers will decide to reskin everything and anything not using their native toolkit will look out of place. So my app takes its inspiration from Twitter Bootstrap and just doesn't even try to look native. You can skin JavaFX with CSS so it's quite easy to match the look, at least in some ways. Nobody has complained and quite a few people said the app looks great. I would definitely do this again for my future apps. Pick a nice design that isn't native to any platform in particular, and people won't hate you for it.
BTW Java now comes with a packager tool that makes self contained native installers which don't depend on the user having Java installed. Deployment is a lot more practical these days.
Although there are skins that can make it look native on each platform, I didn't bother with this for my app. Trying to match native on a cross platform app is a fools errand. A few months after you ship your app, the OS developers will decide to reskin everything and anything not using their native toolkit will look out of place. So my app takes its inspiration from Twitter Bootstrap and just doesn't even try to look native. You can skin JavaFX with CSS so it's quite easy to match the look, at least in some ways. Nobody has complained and quite a few people said the app looks great. I would definitely do this again for my future apps. Pick a nice design that isn't native to any platform in particular, and people won't hate you for it.
BTW Java now comes with a packager tool that makes self contained native installers which don't depend on the user having Java installed. Deployment is a lot more practical these days.