Having flown the route on both in the past year, my 2c

Food

• Cathay is better out of Heathrow for the most part. It's also Do&Co, so it's more the variety of asian dishes that make it better.
• Out of Hong Kong at certain times, Cathay have a supper service. There is no starter, unlike BA.

Service

• Cathay service has a low baseline. There was not one positive moment. They were slow, inattentive, and never to be seen outside of meal service.
• BA is more variable, although generally better in my experience. I think the average is higher than Cathay although it's more likely you'll get much worse.

Seat

• The Aria Suite is much better and more advanced than the Club Suite. The Club Suite is better than the old Cathay seat.

Lounges

• Lounges out of Hong Kong are the same for both, and excellent.
• No arrivals lounge in London for Cathay.

Next time, I will fly BA for the tier points. Lounges are identical out of HK. I can sacrifice the Aria Suite to not wait 2 hours for a drink on an overnight flight.