I am posting this response several years after the fact since the information contained above did not match my personal experience. I live in the foothills of Denver, CO where we routinely see high winds and where shadowbox fencing is preferred for its apparent wind shedding characteristics. I am also a mechanical engineer and in need of a new fence after ours was blown over (a double sided solid picket fence) and while I had not previously investigated the issue, I thought an experiment and some calculation might be in order.
While surface area is an important scaling factor in fence design there is another factor that is being ignored here witch is the Coefficient of Drag, which scales 1:1 the same way surface area does. Drag Coefficients are typically numbers between 0 and 1 for structures, so if a structure has a drag coefficient of .5 it will have half the force applied for a given wind speed when compared to a structure with a drag coefficient of 1.0.
I mocked up both a solid picket fence as well as a shadowbox fence with Popsicle sticks and bass wood for the stringers. They were attached to a 3d printed test stand via rubber bands (see image) Each was constructed with the same surface area and subjected each to "wind blasts" from the exhaust of my shop vac.
Each fence section was alternated in the test jig and tested 5 times for a total of ten tests. The deflection of the fence section due to the wind was measured with a .25mm scale at both the top and the bottom of the fence section during each test.
The results were consistent from test to test with the shadowbox fence demonstrating less than half the total deflection of the double sided picket fence.
Given that the surface area, air velocity and air density were the same for each test, and that the alternating of samples from one test to the next would eliminate any variability of the jig/test setup. I am fairly confident that the shadowbox fencing has better resistance to wind loading.