Magnetorheological elastomers (MREs) are a re-emerging class of smart materials whose novel behavior stems from their response to magnetic fields. Historically comprised of soft-magnetic carbonyl (spherical) iron particles embedded in highly compliant matrix materials, MRE research has focused on their apparent change in shear modulus (in excess of 60%) under a magnetic field. Recent work by the authors has departed from the experimental and theoretical focus on MREs made from soft-magnetic particles (S-MREs) to investigate MREs having hard-magnetic particle inclusions (H-MREs). While H-MRE materials do not perform well in dynamic shear stiffness applications when compared to the traditional S-MREs, H-MREs provide remotely powered, fully reversible actuation capabilities that S-MREs are unable to achieve. In addition, in the same dynamic shear stiffness applications these H-MREs provide a measure of active control of which S-MREs are also incapable. This work examines the role that particle magnetization, developed due to shape anisotropy, plays in the actuation response S-MREs in contrast to H-MREs. H-MRE response is predicated on the response of the hard-magnetic particles to the external magnetic field and to neighboring particles. Since hard-magnetic particles have an internal preferred magnetic orientation, they are able to generate torques at the particle level, T=M x B, where T is the torque density, M is the magnetization, and B is the local magnetic flux density. In contrast, soft-magnetic particles may develop an induced magnetization when exposed to an external field if the particles exhibit shape anisotropy. This induced magnetization is also capable of producing torque at the particle level, however, spherical particles like those historically used in MREs are geometrically isotropic and therefore do not develop induced magnetization either and consequently the widely studied MREs comprised of soft-magnetic spherical particles generate no torque at the particle level. Shape anisotropy further complicates the mechanical response by inducing Eshelby-type shape-dependent effects on the mechanical stresses developed local to the particle. These effects vary the local particle rotation, resulting from a given macroscopic loading, and in turn affect the local magnetic field by changing the particle's magnetization axis with respect to the external field. The result is a material system whose elasto-magnetic response depends on particle shape and orientation as well as on particle magnetization. In previous works the authors used barium hexaferrite (a hard magnetic material) and carbonyl iron powders to generate MRE materials having varying particle alignment and magnetization permutations. These materials were examined in cantilever bending modes to assess and differentiate their abilities as bending actuators. In this work, finite element studies mirroring the bending tests are performed to determine the role of particle/magnetization anisotropy on the behavior. Results show strong dependence on particle shape anisotropy.