The operational characteristics of a magnonic crystal, which was fabricated as an array of shallow grooves etched on a surface of a magnetic film, were compared for magnetostatic surface spin waves and backward volume magnetostatic spin waves. In both cases the formation of rejection frequency bands was studied as a function of the grooves depth. It has been found that the rejection of the volume wave is considerably larger than of the surface one. The influences of the nonreciprocity of the surface spin waves as well as of the scattering of the lowest volume spin-wave mode into higher thickness volume modes on the rejection efficiency are discussed.