For me LWJGL used tobe faster. But it seems to depend on the system. A few people reported better performace for JOGL_AWT.
LWJGL was faster than JOGL 1.1.1a on some machines, slower on others. However, JOGL 2.0 with NEWT is at least as fast as LWJGL.
I think, JOGL supports the most platforms. Though I haven't followed its developement in recent time, nor taht of LWJGL. But LWJGL always used to support these three platforms, that you mentioned.
JOGL 2.0 supports Windows, Mac OS X, Unix (Solaris, OpenIndiana), GNU Linux and Android. Its native windowing system works very well and allows to work around AWT bugs