The stiffness depends more on the shape of the rim, in particular the rim depth, than the material. So a shallow depth rim is less stiff in the vertical plane, thus provides a smoother ride on rough roads,,,hence the old school shallow tubular rims used by the Pros on cobblestones races such as Paris-Roubaix. A 30 mm deep aluminum rim can be quite stiff compared to a 25 mm deep carbon rim...