Well, the choices range from Y+ hardware with Y software i.e. economy level service throughout to Y+ hardware with J software. I'd be surprised if they do the latter as that's expensive to deliver. Same goes for a specific Y+ service level between Y and J as that raises the complexity of service delivery (= costly) e.g. 4 different categories of meals instead of 3, crew needs to deliver 4 different levels of service, 4 types of amenity kits. So the probability is Y+ hardware with perks that are cheap to deliver such as Business class check-in and luggage allowance.

BA delivers the former i.e. Y+ hardware with Y software, but gives 1.1x mileage on Y+ so I'd guess CX will have to offer the same mileage rate to stay competitive.