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Strain localization in the lithosphere and the formation, evolution, and maintenance of resulting plate boundaries play a crucial role in plate tectonics and thermo‐chemical mantle convection. Previously activated lithospheric deformation zones often appear to maintain a "memory" of weakening, leading to tectonic inheritance within plate reorganizations including the Wilson cycle. Different mechanisms have been proposed to explain such strain localization, but it remains unclear which operates on what spatio‐temporal scales, and how to best incorporate them in large‐scale mantle convection models. Here, we analyze two candidates, (1), grain‐size sensitive rheology and, (2), damage‐style parameterizations of yield, stress which are sometimes used to approximate the former. Grain‐size reduction due to dynamic recrystallization can drive localization in the ductile domain, and grain growth provides a time‐dependent rheological hardening component potentially enabling the preservation of rheological heterogeneities. We compare the dynamic weakening and hardening effects as well as the timescales of strength evolution for a composite rheology including grain‐size dynamics with a pseudo‐plastic rheology including damage‐ (or "strain"‐) dependent weakening. We explore the implications of different proposed grain‐size evolution laws, and test to which extent strain‐dependent rheologies can mimic the weakening and hardening effects of the more complex micro‐physical behavior. Such an analysis helps to better understand the parallels and differences between various strain‐localization modeling approaches used in different tectonics and geodynamics communities. More importantly, our results contribute to efforts to identify the key ingredients of strain‐localization and damage hysteresis within plate tectonics and how to represent those in planetary‐scale modeling. Key Points: Comparative analysis of strain localization and damage memory for grain‐size dependent and strain/damage parameterized rheologiesIdentification of key ingredients of strain localization and damage hysteresis and how to represent those in planetary‐scale modelingPlastic strain softening enables hysteresis with a memory duration similar to grain growth at lithospheric temperature conditions [ABSTRACT FROM AUTHOR]