To Unsound: to use my analogy above, the point to a horn is that the air is unable to "escape" away from the radiating surface of the driver, that is, to just move to the side and out of the way of the driver, thus unloading it. In a horn, the gradual expansion forces the driver to load a much greater volume of air directly in front of it, and doesn't "release" the driver from this loading until the horn mouth opens into the room, at which point the surface area that the air is pushing against is immense. True horns are so efficient at loading their drivers that they require what are called compression drivers, which are designed to deliver much higher than normal force at much lower than normal excursions.
To Zaikesman and Pmwoodward: a stiff vs. flexible cone mostly affects the fidelity of the signal, not the inherent efficiency of the driver. That, as I said, is mostly dependent on magnet force and moving mass. Of course, enough flex will result in energy being dissipated as heat within the cone itself, which lowers the efficiency, but very few drivers flex enough to do this within their designed passbands. They will do it as they start to break up at the top of their range, but hopefully the crossover has taken over by then.