Let's say for example QR cancelled a flight KUL-DOH (as they did for me) as part of a itinerary back to the UK.
As I had booked with Avios via QR an agent was able to rebook me from HKT instead at no extra charge.. even though there was no availability.
I believe had it been BA I would have been stuck with whatever QR had automatically rebooked me on. BA wouldn't have been able to rebook me on the HKT flight as they'd have needed availability.
So even though I find the BA call centre experience much better I'd probably book a QR reward via QR.