We investigate the impact of various phonon scattering mechanisms on the in-plane thermal conductivity of suspended silicon thin films with two-dimensional periodic arrays of holes, i.e., phononic crystal (PnC) nanostructures. A large amount of data on the PnC structures with square, hexagonal, and honeycomb lattices reveals that the thermal conductivity is mostly determined by the surface-to-volume ratio. However, as the characteristic size of the structure is reduced down to several tens of nanometers, thermal conductivity becomes independent of the surface-to-volume ratio, lattice type, and other geometrical parameters, being controlled solely by the distance between adjacent holes (neck size).