Different models of finite strain plasticity with a nonlinear kinematic hardening are analyzed in a systematic way. All the models are based on a certain formulation of a rate-independent Maxwell fluid, which is used to render the evolution of backstresses. The properties of each material model are determined by the underlying formulation of the Maxwell fluid. The analyzed approaches include the multiplicative hyperelastoplasticity, additive hypoelasto-plasticity and the use of generalized strain measures. The models are compared with respect to different classification criteria, such as the objectivity, thermodynamic consistency, pure volumetric-isochoric split, shear stress oscillation, exact integrability, and w-invariance.