<p>I am trying to achieve better performance for my Java SWT application, and I just found out it is possible to use OpenGL in SWT. It seems there are more than one Java binding for OpenGL. Which one do you prefer?</p>

<p>Note that I have never used OpenGL before, and that the application needs to work on Windows, Linux and Mac OS X.</p>

Personally, I'm not even aware of Java bindings for OpenGL other than
JOGL
-- I think JOGL is pretty much the standard for Java OpenGL.
It works in Windows, Linux, and OS X, but you might want to read over the official documentation for some notes about specific issues in each platform.
Keep in mind that the OpenGL paradigm is quite different from Swing/AWT or the Java 2D API; OpenGL is not a drop-in replacement for Swing.