Should I choose the Mercedes or the BMW? That's a nice problem to have. I've flown JL 777-300 ER first class JFK-NRT and CX 777-300ER first class JFK-HKG and HKG-SFO. You can nitpick differences but both are superb. The JL seats are slightly smaller than CX because JL has eight seats in first (1x2x1) and CX has six (1x1x1). I like the sliding auxiliary tray table on the JL seats and the video screen seems bigger. Someone commented on the lack of overhead bins in the first-class CX cabin. I think this is a nice feature as it gives the cabin a roomier look and feel and it is easier to stow carry on luggage in the individual closet at each seat (as well as hang your clothes when you change into pjs).

One other item to factor into your decision should be the lounge. Here CX has a distinct advantage IMO. The Pier lounge in HKG is really special. It has an a la carte restaurant, massages, etc., etc. The JL first-class lounge at NRT is also really nice. It too has massages and two sushi chefs who prepare fresh sushi at the sushi bar. Look up these lounges on the airline websites.

You cannot make a wrong decision.