We present results from a combined experimental and numerical investigation of the fluid-structure interaction of cantilevered porous flexible strips, towed through a fluid bath. We characterize the steady-state deformation of the strips and their associated drag, focusing on the low and moderate Reynolds (Re) number regimes. Our microfabricated strips offer independent control over porosity and permeability, a feature not available in previous studies. We fabricate strips with different levels of permeability, spanning over two orders of magnitude, while fixing their porosity at 50%. Then, the vertically clamped porous strips are towed inside a viscous bath. In parallel to the experiments, we model the strip as an elastica that is loaded locally by low (or moderate) Reynolds forces, via local drag coefficients. At low Re, we find that the drag coefficient, which can be obtained from Stokes simulations of rigid strips under perpendicular flow, varies with permeability by less than 10%. By contrast, at moderate Re, the drag coefficient depends significantly and nonmonotonically on permeability. Whereas porosity dictates the drag coefficient at low Re, our results demonstrate that a precisely designed permeability plays a major role at moderate Re, enabling large variations of the drag coefficients at a set level of porosity. Since porosity is directly linked to weight via the density of the effective solid, understanding how porous structures of fixed porosity and varying permeability interact with the surrounding fluid is of relevance to flying insects and microdrones.