For OpenGL APIs, both LWJGL and JOGL are very capable. I personally recommend LWJGL because of stuff like TWL and jME that works on top of it. JOGL has its own widget sets and engines, but those two are best of breed (if only the former had more documentation).
Some engines support both LWJGL and JOGL, for example JMonkeyEngine 2.0 (contact me in PM if you need some support of JMonkeyEngine 3 for JOGL) and Ardor3D. That's true for NiftyGUI too (I wrote its JOGL 2.0 backend). TWL only works with LWJGL but it would not be that hard to port to JOGL thanks to NEWT. JMonkeyEngine has a large community and a nice game development environment based on Netbeans RCP but I find this engine less reliable than Ardor3D.
JOGL has a few build-in widgets but they require shader support
I agree with kappa, LibGDX and Slick are worth a try too.
Agile2D is very similar to Java2D.
As far as I know, you can use Swing components with JOGL and LWJGL.
Maybe look at this too:http://www.java-gaming.org/topics/hello/24411/msg/205141/view.html#msg205141