It has become the norm here to write about BA F as if it were as pleasurable an experience as a few weeks chained up in a medieval dungeon, whereas Qatar's J product is lauded as unbelievably luxurious. The truth, however, is that BA's first class product is much better than Qatar's business product, and actually I would prefer the A350 as it is to the Q Suite - despite the hype I found that cramped and fairly unremarkable.
So given the the relatively modest price differential I would be choosing BA. I assume the flights are of more even length under the BA option too - which I would prefer personally - but if so the product you'd get on the first leg is far more important a factor than that on the short second flight if you choose Qatar.