for me the difference is that First class is about the personal journey, making things elegant, nice, helpful, your own personal space to relax, to be able to take up more space, being allowed to take the time you want, and accommodating for the individual passenger (AKA- they treat you as a human as opposed to a business class passenger).
business class is about having a flat bed, eatable food, and minimal, but sufficient space to work/be in, -efficiency and speed.
I had a bad experience with 8 BA
FIRST flights a took a few years ago and don't plan on paying the difference anytime soon, and the business class cabin gives you everything you need to get from point A to point B well rested and ready to go then for that, but if you want to have the feeling of being personally looked after where the journey between A and B is something special then go for FIRST. but its a gamble really.
Hope you have a great flight one way or another.
Also- not sure of the mileage difference but if I had choice (and a bit more time for travel) I'd use my BA
miles for CX LHR
First suite far outweighs the BA
seat (new or old) and if it's the same price as BA
First then I'd take that in a heart beat.