According to my college physics 101 professor, a curved sail is generally superior in all situations. There are sails made out of rigid materials, and they generally are curved, even though they could be flat. Everybody who sails knows that you can adjust the slack in your sail, and that sometimes a tighter sail is better, for example when tacking. You can tell this just from the feel.

Now, then, it's been a LONG time since my physics 101 class, but the explanation was something like this: Although this is an oversimplification, you can imagine that a sail works when air particles bounce off of it. The momentum imparted to the sail depends not only on the direction that the wind is coming from, but also the direction that it ends up going when it bounces off the sail. A curved sail helps redirect the wind away from the sail in exactly the direction that the sail is pointing, which is better at pushing the vehicle in the correct direction.

Another way to look at this is if it is a pure matter of air pressure. A curved surface will be better at creating air pressure inside the curve. It's like if you're driving and you hold something out the window. When you hold a rigid board out of the window, it will be hard to hold in place, but the air pressure won't build up behind it as much as a sack, for example. If you hold a sack out the window, it will probably just be ripped out of your hands.