I am silver BA and gold QR,
QR you pay taxes on but not so high. when I use my points for a flight LHR to HKG it was around 200 pounds.
on QR if gold you are guaranteed a reward seat on any flight, however often get stung for double points usage on 1 leg if Doha is not your final destination, if trying to book less than 3+ months in advance. you wont get that on BA,
Not sure if QR will be Avios or not, maybe BA will welcome it as another airline they can dump BAEC members on who can never get a points flight on CW.