Cyclic loading on granular packings and amorphous media leads to a transition from reversible elastic behavior to an irreversible plasticity. In the present study, we investigate the effect of oscillatory shear on polycrystalline and amorphous colloidal solids by performing molecular dynamics simulations. Our results show that close to the transition, both systems exhibit enhanced particle mobility, hysteresis, and rheological loss of rigidity. However, the rheological response shows a sharper transition in the case of the polycrystalline sample as compared to the amorphous solid. In the polycrystalline system, we see the disappearance of disclinations, which leads to the formation of a monocrystalline system, whereas the amorphous system hardly shows any ordering. After the threshold strain amplitude, as we increase the strain amplitude both systems get fluid. In addition to that, particle displacements are more homogeneous in the case of polycrystalline systems as compared to the amorphous solid, mainly when the strain amplitude is larger than the threshold value. We do not see any effect of oscillation frequency on the reversible-irreversible transition.