Well, I really don't know why you need integration with gtk and qt. There are basically 4 main options when you talk about desktop gui in java.
AWT is very outdated, don't use it unless you really need to
SWT is much better, you get a ui that looks like Eclipse (written with SWT). Many people claim that this is faster than Swing (see Option 3)
Swing is part of the standard java libraries. It was developed as a replacement for AWT. Very hard (~ 12-13 years). An independent platform in implementation (your widgets look the same on all operating systems). In modern versions of Java, pretty fast. Very flexible. I would recommend using Swing or SWT if you need to use java. I like Swing more, but my only opinion is mine. Disadvantages - “as is” requires a lot of coding, and you don’t see how your page looks (without markup). Does not use any scripting language. On top of Swing, you can use things like Apache Pivot, but that's a completely different story.
Java FX. Designed as a “next generation ui” platform. requires a java fx compiler (this is not Java code, but what compiles to bytecode). It looks very good, and in itself a great platform, it can be considered as a competitor for Flex and Silverlight. The main disadvantage is that it is not so widespread, because it was too late after its competitors. As a result, it has a relatively small community.
I don’t know about integration with QT / GTK, so I can’t tell you a lot about it
Hope this helps