This paper compares the accuracy of two methods to identify a linear representation of a power system: the traditional Eigensystem Realization Algorithm (ERA) and the Loewner Interpolation Method (LIM). ERA is based on time domain data obtained using exponential chirp probing signals and LIM system identification method is based on frequency domain data obtained using sinusoidal probing signals. The ERA and LIM methods are evaluated with the noise produced by the nonlinear characteristics of the system, these characteristics are caused by increasing the amplitude of the applied probing signal. The test systems used are: the two-area Kundur system and a reduced order representation of the Northeastern portion of the North American Eastern Interconnection. The results show that the LIM method provides a more accurate identification than the ERA method.