SWT by itself is pretty low-level, and it uses the platform's native widgets through JNI. It is not related to Swing and AWT at all. The Eclipse IDE and all Eclipse-based Rich Client Applications, like the Vuze BitTorrent client, are built using SWT. Also, if you are developing Eclipse plugins, you will typically use SWT.
I have been developing Eclipse-based applications and plugins for almost 5 years now, so I'm clearly biased. However, I also have extensive experience in working with SWT and the JFace UI toolkit, which is built on top of it. I have found JFace to be very rich and powerful; in some cases it might even be the main reason for choosing SWT. It enables you to whip up a working UI quite quickly, as long as it is IDE-like (with tables, trees, native controls, etc). Of course you can integrate your custom controls as well, but that takes some extra effort.