Grid adaption is a popular method to enhance the resolution of flow field and the precision of numerical simulation, which automatically optimizes the grid distribution instead of manual complicated work. There exist usually two grid adaptation methods, the feature based grid adaption and adjoint based grid adaption, the former focuses on shocks, vortexes and other features of flow field, and the latter focuses on lift, drag and other aerodynamic characteristics. The comparison of adjoint based grid adaption and feature based grid adaption method is investigated in this paper. Numerical simulations show that both feature adaption and adjoint adaption could improve the resolution of flow field and the precision of numerical simulation such as lift and drag. As for the flow features, the feature adaptation could capture the obvious shock waves and vortexes in the flow field, the adjoint adaptation, however, only captures the flow features that are contributory to the accuracy of aerodynamic characteristics. As for the aerodynamic characteristics, some shock waves and vortexes have little influences to the forces, so the feature adaptation is not efficient as adjoint adaptation, which could greatly improve the accuracy of aerodynamic characteristics.