Boeing has always been the major leader in the commercial aircraft industry but I think that now Airbus is in better shape than Boeing, because they have less orders from Asian airlines than Boeing have and Airbus is selling airplanes to customers for cheap prices. A lot of Asian airlines have deferred or canceled their orders, most of the planes ordered are from Boeing. I think that the Asian recession is what affects jobs at Boeing the most.
Why did BA choose the A320 over the NG737? The Boeing 737 is by far the best selling jetliner in the world, OK I agree with that, but the A320 is also a great airliner and it is doing very well. A lot of airlines in Europe and even in North America are buying a lot of Airbus narrowbody planes, they love the A320 because it's very quiet and very comfortable inside. The A320 and all of its derivatives (319 and 321) are the widest narrowbodies ever built. The 737 has reached now 4000 orders but you can't compare that with the A320 because the A320 came out two decades later. In other words, you cannot judge the B737 vs the A320 in terms of orders received. I'm convinced that the A320 will have more orders that the 737 and will be the other best selling jetliner in the longrun. In two words, the A320 family will beat the 737 in terms of orders. That is the impression that I have. I don't know if you notice but a lot of airlines who have previously bought 737's are now choosing the A320 over the NG737's. Look at United, look at Lufthansa, look at US Airways,...
Now, regarding the widebodies, the 747-400 is the aircraft that has the longest range and passenger capacity. I wouldn't say that the A340 would compete with the 747 because the 747 is in a class of its own. The A340 is the opponent of the 777. If the A3XX becomes reality then it will compete with the 747-400. The 767 and 777 are very reliable airplanes, I absolutely agree...so are the A330/A340. But I think that Boeing will keep the 767 and 777 in production for a long time because they are reliable and efficient aircrafts for the North Atlantic operations (ETOPS). The 767 and the 777 are the best two airliners boeing has made. Boeing is still the largest airliner manufacturer despite the Asian recession but Airbus is doing very well in the short and medium haul narrowbody market, as explained above.
Conclusion: It's hard to predict whether Boeing or Airbus will become the largest aircraft maker because they both build great airplanes and the smallest one, Airbus, is now in better shape than Boeing. Boeing's widebodies are magnificient airliners but I'm convinced that in the far future Airbus will beat Boeing especially if the A3XX becomes reality and receives many orders. Airbus is doing great.