The interaction between a magnetic domain wall and a pinning site is explored in a planar nanowire using micromagnetics to reveal perturbations of the pinning energetics for propagating domain walls. Numerical simulations in the high damping ’quasi-static’ and low damping ’dynamic’ regimes are compared and show clear differences in de-pinning fields, indicating that dynamical micromagnetic models, which incorporate precessionally limited magnetization processes, are needed to understand domain wall pinning. Differences in the micromagnetic domain wall structure strongly influence the pinning and show periodic behaviour with increasing applied field associated with Walker breakdown. In the propagating regime pinning is complicated.