I stuck with BA when i moved to Hong Kong, despite flying Cathay almost exclusively now. BA is easier to earn status on providing you dont fly deep discount economy and you can manage the 4 flights per year on BA metal requirement.

For accumulating and using Avios/Asiamiles, given that your parents are London based they will probably find it easier to find redemptions with Avios.

Third point - Cathay inexplicably charge US$50 to join the Marco Polo Club.