CX is a 1-2-1 configuration, which works well in my experience both for single people (in a window seat) and couples (in the two center seats). JL is in the process of upgrading their J product. The old J is paired angle-flat that are very outdated. The new J is innovative, with side aisles providing direct aisle access from each seat. The new JL J seats have more privacy than CX's J, with a partition that can be lowered for two people traveling together.

I think JL has a larger video screen.

The CX seat feels more spacious, while the JL seat feels more private. In CX, you see other passengers while seated, while on JL you don't see them (nor they you).

JL has more usable space and storage space. Some CX J seats have an open area under the ottoman, but it can't be used during taxi, takeoff, or landing. Most seats are closed under the ottoman. Whereas JL has a shelf and more storage. (The shelf is on front of you in a window seat, and along side you in an aisle seat, but the aisle seat has part of its shelf area taken by the video controller of the window seat.)

Service is excellent for both. Food preference is very personal; some people will prefer food on JL while others that on CX.

If it's a choice between CX J and JL old J, go with CX no question. If the choice is between CX J and JL new J, I'd suggest trying one each way if you can.