A symmetrical wing is better for inverted flight but there are other factors which can over-ride this. In full size I usually fly aerobatics in a Robin 2160. This has a symmetrical wing. Sometimes I am lucky enough to fly a friend's Yak52 which has a flat bottomed wing. Yet the Yak is by far the better handling plane when inverted. This is due to balance points, stability etc, the Robin being designed for mass market private fliers whereas the Yak is designed for the strictly controlled and selected world of military fliers.

Although some previous posts have mentioned that the upper surface is longer than the lower surface even for a symmetrical wing with an angle of attack, this has nothing to do with lift. Air molecules which separate at the leading edge do not meet again at the trailing edge, there is no need for them to alter speed so that they meet up again. Unfortunately this story is still often printed in books and model magazines.

There are pressure differences around a wing and these are related to the fact that the flow is turned in a different direction. Changing direction is a velocity change. Bernoulli's law states that the sum of the energies of velocity and pressure must remain the same if no energy is added or removed, so if velocity changes then pressure must change in the opposite way.
NASA's Glenn Research Centre kindly puts all this on the web for you, see www.grc.nasa.gov/WWW/K-12/airplane/right2.html keep following the links and you will also find the pages where NASA explains why a wing is not a venturi. By turning the flow downwards to get downwash, we have a change of velocity which Bernoulli tells us must go hand in hand with a pressure change.

Before anyone jumps on this as a Bernoulli versus Newton thing, you should be aware that Bernoulli's Law is a purely Newtonian law! Newton gave us the general laws about the conservation of mechanical energy, Bernoulli's Law is simply a specific case of this law as it applies to a gas's mechanical energy. Bernoulli versus Newton is therefore impossible! Anyway, the paragraph above tells you that both downwash and Bernoulli go together.

Bernoulli is usually misunderstood to have said that in a venturi, the speed rises and causes a pressure drop. He said no such thing. For the speed to rise, a force must be applied. If no energy is being added or removed, where did the force come from? The pressure drop of course. So the pressure drop caused the speed to rise. But why did the pressure drop? Because the speed rose! And round and round it goes. Neither is the cause of the other, both of them are co-incident effects of a venturi and Bernoulli simply gave us the equation that relates the two effects. It's like engine noise and exhaust smoke, neither is the cause of the other, they are both effects of something else, yet there is a relationship between volume of noise and the amount of smoke. More noise goes hand in hand with more smoke but we don't say that noise causes the smoke.

Harry