From my personal experience, the new BA seat, headphones, and first meal are much better. CX has better IFE content, second meal & snacks, LHR lounge, and general recognition of Golds (IFL welcome, J drink etc)

BA Golds get first dibs on front row in WTP (calf rest), and *much* higher likelihood of upgrade, esp during "holiday season" - Y is more heavily overbooked on BA (and smaller), so Goldies are first in line Y-to-WTP, WTP-to-CW, CW-to-F - I think I've had more upgrades than not on BA to/from HKG... BA is A350/789 (pressurised to lower altitude so less drying and less jetlag, plus CWS if upgraded on A350) while CX is mostly back to 77W now (bigger, noisier, more jetlag)

Material schedule reliability difference if this matters to you: outbound CX is more likely to be delayed getting to the gate at HKG (CX pilot friends-of-friends are deliberately doing the go-slow to up their paid flying hours, no really...), but BA inbound can be frustratingly slow because it lands so early (nobody to do stand guidance, need to silence engines because noise curfew and then wait for tug etc)