Singapore airline is the far superior of the two if flying economy. I'm not sure if they do the route but Virgin Upper Class is better then BA First class if yo want something with a little more legroom
I wouldn't bother choosing an airline, the best thing to do is to use a broker who will be able to get you some really good deals on the price, I can recommend 'Trailfinder' they got me some excellent deals, that is unless you can afford to choose your airline! hope your trip's good.