Magnetorheological elastomeric (MRE) composites composed of a silicon rubber matrix with dispersed Co particles of different morphology and weight fraction: (a) spherical microparticles of 10, 30, and 50 wt% and (b) nanowires of 10 wt% were subjected to compressive pre-strain with normalized amplitudes of 1, 2, or 3 % while held in the magnetic cell. The deformation frequency ranged from 0-20 Hz, while the magnetic flux density was fixed at discrete values of 0, 0.1, and 0.2 T. Our investigation of the spherical microparticle-based composites show that the dynamic stiffness and equivalent damping increase with the particle weight fraction for all strain amplitudes. The most significant magnetorheological (MR) effect on dynamic stiffness is observed for 10 wt% samples at strain amplitude of 1 %. This effect highly decreases with both weight fraction and strain amplitude. The MR effect on equivalent damping is much higher than that on dynamic stiffness and it only slightly decreases with particle weight fraction and strain amplitude. To assess the dependence of MR properties on Co particle morphology, the 10 wt% spherical microparticle- and nanowire-based composites were compared. The dynamic stiffness and equivalent damping coefficient values are much higher for the nanowire-based MRE compared to the spherical microparticle-based MRE for all strain amplitudes. However, the MR effect on dynamic stiffness and equivalent damping coefficient is slightly smaller for the nanowire-based composite.