The current differential protection of power lines is based on the RL lumped parameter line model and the principle of charge continuity. The traveling wave differential protection of power lines is based on the distributed parameter line model and the principle of traveling wave transmission invariance. This paper conducts a detailed comparative study on these two types of differential protections for application on power lines from the view of theory and simulation. The essential difference between the above two protections is that the traveling wave differential protection considers the distributed parameter characteristic and the spatial propagation characteristic of a line, whereas the current differential protection regards the line as a node and completely neglects the distributed parameter characteristic and the spatial propagation characteristic of a line. In fact, the differential current is the degradation form of the traveling wave differential current. For UHV long distance transmission lines, the traveling wave differential protection has a superior performance over the current differential protection. For HV and EHV transmission lines, there is no significant performance difference between the traveling wave differential protection and the current differential protection. The current differential protection is qualified for this kind of transmission line. This work is supported by National Key Research and Development Program of China (No. 2016YFB0900600).