Double-walled rim's what difference depth makes?

Mostly aerodynamics. Generally the deeper the rim, the less drag a wheel has. High-end aerodynamic wheels have carbon rims with 80mm or more rim depth. On the extreme end you have disc wheels. Of course a possible disadvantage is weight. Another possible disadvantage is susceptibility to side wind (not really a problem with 30mm depth, but certainly a thing with 80mm depth on the front wheel).

The reason why wheels with deep rims have less drag is mostly turbulence. When you look at a bike head-on you don’t even see the wheels, since the tires are wider than the rims. So it’s not “traditional” head on drag. The spokes create turbulence and the upper, outer parts of a wheel are actually traveling at twice the bike’s velocity against the air. Making this area as flat and smooth as possible (i.e. deep rims, few spokes) helps reduce turbulence. It also helps when the transition from tire to rim is smooth, which is one of the reasons why modern road bike rims have gotten much wider and now generally smoothly attach to a 25mm tire without the tire bulging outwards. The teardrop cross-section of the rim also helps to delay flow separation.

I think deeper rims can also be stiffer (radially), allowing for fewer spokes.

This website shows a very strong correlation between rim depth and reduction in drag. Older version of the diagram here:

I think the large differences among low depth wheels are mostly down to spoke count, spoke type and to a lower degree shape (and width) of the rim. Would be interesting to plot cost, weight, stiffness and strength until failure on the same diagram.