I worked on Java apps around that timeframe. Despite spending a lot of effort refining our widgets and using some animated transitions (ref the "Filthy Rich Clients" book) the applications generally felt more dated and cheaper-looking than native apps.

For enterprise apps with no strong competitors these minor aesthetic issues didn't impact revenue so those UIs remained in Java. But for everything else it was worth it (financially) to migrate to native.

I sometimes armchair quarterback and wonder whether Java would have been more successful if the Swing folks had focused more on design. It seemed like the most they ever did UI wise was attempt to catch up to platform native widgets so they were perpetually several years out of date and slightly inconsistent. Had they skated to where the puck was going to be rather than where it is perhaps Java applications would be the ones people pointed to when asking devs to "make it look sexy" instead of iTunes.