I've flown dozens and dozens of QR segments and BA segments the past year and here is my takeaway.

Comparing BA J to QR J and NOT looking at status (using LHR GF as a Gold)
QR J dine on demand is a great option including on the ultra long haul flights. You can balance out TV time, sleep, and food. QR J food is superior to BA J, but I was quite impressed with the Do&Co catering the other day on my LHR-JFK flight. Once they get the timing down (almost 3hrs to serve dinner is way too long), I would say it would be a contender for QR J food.
Seat wise, I prefer the QR 777 series over their Airbus. Yes, I know that the airbus have newer seats and a more privacy, but the 777 have so much space. And BA J, even being outdated, I prefer over the tiny foot hole that most new J cabins have.
Entertainment wise, I'd had many issues with the BA system (either reboots or being down the whole flight).
And lounge wise, Al Mourjan beats BA galleries club out of the water. Between the nice buffet area, sandwiches, sleeping rooms, showers that don't sound like a pissed off dog, etc, it's a pleasure to connect in DOH (and the bear is a added bonus )
If you factor in BA GF lounge, better booze in the GF lounge than Al Safwa, and BA CS (id had only Excellent treatment from the GGL line), then it really becomes hard to pick.

But simply, it's at least an extra 140 tps to connect in DOH