A top-down approach using focused ion beam has been employed to fabricate Co/Permalloy hard-soft bilayer magnetic antidot arrays. These nanopatterned films are studied with particular emphasis on magnetic coercivity. The antidots have a diameter of 40 nm and the studied antidot symmetries are square and hexagonal. A dependence of magnetic coercivity on the relative thicknesses of the magnetically hard (Co) and soft (Permalloy) layers is found; increasing Permalloy thickness results in lower magnetic coercivity. Furthermore, the long-range periodicity of top-down nanopatterned antidots results in higher magnetic coercivity and a stronger magnetic domain-wall pinning, compared to identical hard/soft bilayers of short-range order deposited on porous anodic alumina. The combination of antidot symmetry and hard/soft thickness, allow for efficient tailoring of the magnetic properties of nanopatterned thin films. Finally, magnetic force microscopy imaging of the antidot array magnetic configuration shows striking qualitative differences between the two array symmetries: square symmetry arrays have inhomogeneous magnetic state and a high density of immobile super-domain walls, whereas hexagonal symmetry arrays show a homogeneous magnetic configuration.