Three types of antidot lattices (ADLs) based on a permalloy thin film, with increasing complexity of the unit cell: simple square, bi-component square, and wave-like ADLs were studied experimentally using both ferromagnetic resonance and Brillouin light scattering spectroscopy techniques. An additional small antidot placed in the center of the square unit cell induces significant modification of the ADL spin-wave spectrum and changes its dependence on the orientation of the in-plane applied magnetic field. The introduction of air-gaps connecting small and large antidots transforms the system into the wave-like ADL and results in further changes in the spin-wave spectrum, including a strong discrimination between two mutually orthogonal principal directions of the ADL in terms of spin-wave propagation. We also point out the impact of defected holes on the obtained spectra. The micromagnetic simulations and the calculation based on the plane wave method satisfactorily confirmed the experimental results.