The soul is dyed the color of its thoughts. Think only on those things that are in line with your principles and can bear the light of day. The content of your character is your choice. Day by day, what you do is who you become. Your integrity is your destiny - it is the light that guides your way. - Heraclitus
Both Swing and AWT are platform independant - as long as there is a JVM for that platform.
The thing about Swing that isn't completely platform independant is the look&feels - I've tried but wasn't able to get the GTK L&F to run under Windows, and I guess it will be equally hard to get the Windows L&F to run under any non-Windows OS.