I just booked CW SFO to MAA and BLR for February. I have status on AA and went there first to search for a flight, looking for either BA or Qatar. on AA.com, the BA flight was $17,000. I went to BA.com and paid less than $5000 (which I couldn't exceed for my company to reimburse). I have never seen that much of a price differential before. I called AA about the price difference and the agent didn't have any answers on that kind of price differential.

Great tip on Aerolopa instead of seatguru, thank you! Status saved me ~$500 in seat selection fees.