The emergence, geometry and activation of faults are intrinsically linked to frictional rheology. The latter is thus a central element in geodynamic simulations which aim at modeling the generation and evolution of fault zones and plate boundaries. However, resolving frictional strain localization in geodynamic models is problematic. In simulations, equilibrium cannot always be attained and results can depend on mesh resolution. Spatial and temporal regularization techniques have been developed to alleviate these issues. Herein, we investigate three popular regularization techniques, namely viscoplasticity, gradient plasticity and the use of a Cosserat continuum. These techniques have been implemented in a single framework based on an accelerated pseudo-transient solution strategy. The latter allows to explore the effects of regularization on shear banding using the same code and model configuration. We have used model configurations that involve three levels of complexity: from the emergence of a single isolated shear band to the visco-elasto-plastic stress buildup of a crust. All considered approaches allow to resolve shear banding, provide convergence upon mesh refinement and satisfaction of equilibrium. Viscoplastic regularization is straightforward to implement in geodynamic codes. Nevertheless, more stable shear banding patterns and strength estimates are achieved with computationally more expensive gradient and Cosserat-type regularizations. We discuss the relative benefits of these techniques and their combinations for geodynamic modeling. Emphasis is put on the potential of Cosserat-type media for geodynamic applications.