Hi
JOGL seems to be for scientific purposes. Correct me if I'm wrong, but I haven't seen JOGL being used for games so far.
You're wrong as I already said
here. JogAmp (JOGL, JOAL, JOCL) is used for games too, for example Salem, Poxnora, Cold Contract, ...
There is an example of Minecraft-like game using a subset of Ardor3D with JogAmp
here.
Salem
Megacorps Online (discontinued)
Jake 2
Cold Contract
JogAmp and LWJGL aren't Java engines but rather sets of low level bindings with some utilities and helper classes. LibGDX is a middle level API for 2D and 3D. Ardor3D, JMonkeyEngine, Java3D, 3DzzD, Xith3D, Aviatrix3D, ... are 3D engines written in Java.
Good luck.