Suppression of noise and vibration suppression is important in various fields, such as the living environment, industrial development, and national defense and security. The bandgap properties of phononic crystal metamaterials provide an approach for controlling and eliminating harmful vibrations in equipment and noise in the environment. In this study, we used two types of two-dimensional honeycomb gyroscopic metamaterials: free and constrained. The dynamic equations of the two systems were established using angular momentum and Lagrange theorems. The dispersion relations of the two systems were obtained based on the Bloch theorem, and the influence of the gyroscope angular momentum or gyroscope speed on the dispersion relations was analyzed. Numerical simulations were conducted to analyze the wave propagation characteristics and polarization under different excitation conditions in a limited space for both types of metamaterial structures. The constrained-type and free-type metamaterials were compared, and the regularities of the dispersion relations and wave propagation characteristics by the gyroscope effect were summarized. This study provided a comprehensive and in-depth understanding of the bandgap and wave propagation properties of gyroscopic metamaterials and provided ideas for the design of bandgap modulation in metamaterials.