People will have different opinions on this but I prefer the CX lounge. JL F is a lot noisier and busy. The food menu is very Japanese which may be a positive for you but doesn't do anything for me, I usually get some sushi and go to the CX lounge after. The JALs Salon upstairs is nice if you fancy Japanese whiskey but isn't open all day, I do believe it's open during the hours you'll be there. CX has their noodle bar and some great offerings at it. They also have proper Bloody Mary ingredients, which I enjoy before a morning flight.

If you have time, go to both and form your own opinion.