I expect most people would answer something like "definitely QR".
My opinion is different. QR might have slightly better food, slightly better entertainment and (if you get lucky) slightly better seats than BR.
But here are my reasons why I would go with BR in a heart bit:
1) I find QR flight attendants to be way too intrusive to my taste (arguably out of abundance of care for its customers, but to me it is just too much, way too much). BR flight attendants are caring and are always there, but they are trained to be very discreet and it is the customer who sets how much interaction he or she wants, not the flight attendant.
2) Connecting in TPE is for me a much better experience than connecting in DOH. DOH is something closely related to a flea market (I include here the lounge experience). I find connecting in TPE to be a much smoother and much better experience. In my view, DOH is just a thin layer of shiny kitsch sprayed over a thick pile of s..t.
Also, in DOH you get bussed very often (true, in a separate minibus just for business class passengers, but it still a bus) while in TPE I never had to use a bus.
Another point: if one needs to use a restroom outside the lounge, one would definitely want to find oneself in TPE, rather than in DOH. I won't give details...
3) In case of IRROPS or if one needs to change tickets or one needs to cancel tickets, it is much, much easier (and faster) to deal with BR than QR.
I could list a few other less important reasons. But just for these three, I would never pick QR over BR (unless QR's price would be much, much better).