Field-induced microstructure evolution can play an important role in defining the coupled magneto-mechanical response of Magneto-Active Elastomers (MAEs). The behavior of these materials is classically modeled using mechanical, magnetic and coupled magneto-mechanical contributions to their free energy function. If the MAE sample is fully clamped so it cannot deform, the mechanical coupling is reduced to the internal microscopic deformations caused by the particles moving and deforming the elastic medium that surrounds them. In the present study, we build on a unified mean-field theoretical approach which takes the microscopic elastic energy into account. Combined with experiment, this approach reveals how microstructure evolution affects the magnetization behavior of isotropic MAEs. MAE disks with various matrix stiffness and volume fraction of particles were fabricated and the magnetization curves were measured by vibrating sample magnetometry. We demonstrate that the idea of columnar structures forming from randomly distributed particles upon the application of an external magnetic field provides an effective approach in modeling microstructure evolution in these materials. Our unified mean-field model, using few and physically meaningful parameters, shows good quantitative agreement with the experimental data on magnetization and magnetic differential susceptibility of MAE samples. More importantly, our model can estimate microstructure evolution in highly filled samples, for which measurements are very challenging. Since changes in magnetization and stiffness are both driven by microstructural evolution, a quantitative relationship can be established between the two effects, as they represent different macroscopic manifestations of the same microscopic process. Therefore, our model can be used in conjunction with magnetization measurements to predict the mechanical modulus of MAEs without the need for elastic testing.