CX F is far superior to CX J. JL F is excellent on some routes (comparable to CX F) and not so good on other routes (closer to CX J than to CX F). CX F is mostly the same on all routes, without the large variations of JL F. But for an award you will find difficulty in getting availability on the good routes on either CX or JL F.

Historically JL5/6 JFK-NRT has had one of the very best F services (while the other JFK-NRT flight, forget the flight number, had a considerably worse F service). Some of the JL F service elements have been dropped in the past year (for example, the Sony VR visors are gone, they were too unreliable). Plus some of the JL F service is very japanese (zen-like, contemplating a single grain of rice on a plate kind of service), which while very luxurious might not appeal to western tastes. CX F is more international and you can have as much or as little chinese influence as you want (though some of the best elements are chinese).