We present an experimental and theoretical study of magnonic band gaps in planar one-dimensional magnonic crystals of two types, with a periodic array of metallic stripes or a periodic array of grooves on an yttrium iron garnet film. Propagating magnetostatic surface spin waves are excited in the considered periodic magnetic structures and measured by microstripe transducers with a vector network analyzer and with a Brillouin light scattering spectroscopy. The properties of magnonic band gaps are explained and illustrated by finite element method calculations. We demonstrate a major influence of the nonreciprocal spin-wave dispersion properties induced by metallic stripes on the width of the magnonic band gap and its dependence on the external magnetic field. The indirect character of the band gap and the higher group velocity of spin waves in the metallic magnonic crystal are identified as the main causes of the wider band gap and steeper decrease in its width with increasing magnetic field in this structure as compared to the grooved magnonic crystal. Potential applications of both types of magnonic crystals and prospects for their miniaturization are discussed as well.