Doing the plane task is probably easier, in the long run anyway. There are a lot of very good dogfighters out there, as mentioned already, but they're not on every server. Chances are you'll take another plane down if you keep at it.
It would, however, be worth checking out the videos @x--Fusi--x posted. They should be a big help. I'd also suggest trying to stick with the other pilots on your team (hopefully they'll protect you. You may also be able to finish off someone they're attacking), keeping a good eye on your mini-map for enemy planes getting spotted, trying to prioritise enemy fighters over bombers (if you don't have upgraded guns fighters should go down quicker), and don't stress about it as that'll only make it more frustrating.