When the extended strong tracking filter (ESTF) is used to improve the carrier tracking estimation instead of the extended Kalman filter (EKF), it is found to be difficult to effectively and consistently evaluate superiority of the ESTF than the EKF. The primary cause is that the basic properties of the traditional Kalman filter are broken due to the subjective fading factor. The superiority of the ESTF is customarily shown by simulations and experiments in previous work only and the corresponding mechanism analysis is very lacking. Motivated by this, we study the performance comparison of the ESTF and EKF. First, the statistical parameters such as the prediction mean-squared error (MSE), the MSE, and the gain matrix are analytically and systematically compared in theory. Second, the inconsistency of estimation performances is explicitly revealed based on the comparison results. Third, mismatching analysis of estimation performance expressions, which are the root-mean-squared error and MSE, is briefly presented for the ESTF. The presented results state clearly that the usability of the conventional Kalman filtering theory is seriously limited and its structure is easy to be destroyed. It is a challenge and a good chance to study new performance evaluation methods on the class of strong tracking filters for engineering application.