In this contribution, we present a qualitative and quantitative comparison of two- and three-dimensional finite-element simulations for magneto-rheological elastomers. Based on a general continuum formulation of the coupled magneto-mechanical boundary value problem, a microscopic modeling approach is applied. The merit of this strategy is a full resolution of the local magnetic and mechanical fields within the heterogeneous microstructure of magneto-rheological elastomers—it allows to account for systems with high particle-volume fractions and small inter-particle distances. In order to understand basic deformation mechanisms as well as local magneto-mechanical interactions of the spherical inclusions, the differences between simplified two-dimensional and realistic three-dimensional simulations are initially shown for the example of chain-like structures with varying arrangements of the particles. Afterwards, an appropriate scale transition scheme is used to connect the microscopic and macroscopic quantities: Different two- and three-dimensional, ideal and random microstructures are analyzed with regard to their effective magneto-mechanical behavior.