The Stiffness of the past is just inverted bendiness. So bendiness in the tag is what you are looking for. That is what primarily governs the visual bendiness of the simulation.
Simulating stiff materials with a soft object simulation however needs a lot of iterations and even more when you have higher resolution meshes. If you don't have enough substeps or iterations in relation to the mesh density, it will appear also very bendy and not stiff, because the solver cannot achieve what you have set up for low bendiness for one simulation step and loses against gravity, collisions and other forces on making the cloth stiff. So having high res meshes also requires high substeps and or high iterations in the solver settings, otherwise the low bendiness you've set up cannot be achieved. Invertedly you can say, a lower res mesh is easier and faster to make stiff. If it's supposed to be stiff you luckily often don't need the mesh resolution to show details like wrinkles, so creating a low-res sim is fine. You can always simulate a proxy and transfer the simulation to a higher version with a mesh deformer.