Concerning the clock accuracy, a hack mentionned several times on this forum allows to force Microsoft Windows to use an high precision timer. Therefore, JOGL does not need to implement an API for this, does it?
The more you use the specific helpers and features of JOGL, the harder such a switch will be. I admit that you can easily avoid using the texture API of JOGL but some more evolved features would require much work, for example the new API allowing to draw text and curves on the GPU and it would be the same for the next API for cross-platform (desktop and embedded) GUIs. I have often done the opposite operation (switching projects from LWJGL to JOGL) and it is mainly a matter of time. If you are very comfortable with OpenGL (and sometimes underlying windowing APIs), you can do it.
In my humble opinion, as JOGL and LWJGL are very similar (which is even more true now with JOGL 2.0), as they both provide similar “services” (with a few exceptions), it is not worth it. Some bug fixes are only in JOGL and not in LWJGL, some other bug fixes are only in LWJGL and not in JOGL. Then, some games work a bit better with JOGL, some games work a bit better with LWJGL. It would be fine to identify them more precisely and share our knowledge as I did when LWJGL was no more working on some ATI cards some years ago.
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JOAL works fine too, I just need to perform more tests because Michael Bien claimed JOAL works fine with OpenALSoft but I didn’t check it by myself. The OpenAL binding of LWJGL has been better maintained for years than ours 
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As I said, it is mainly a matter of time. I think porting things from LWJGL to JOGL is quite boring, it would be better if both teams had been able to find an agreement to maintain only a single set of APIs instead of LWJGL on one side and JogAmp on the other side. As time goes by, both projects are taking different roads and such a convergence becomes harder.