This paper has carried out a detailed investigation on oscillatory mode information-based system inertia estimation techniques. In the first step, the critical modes of oscillation are extracted from the post-disturbance frequency deviation signal which is obtained from the phasor measurement units (PMUs). In this process, two popular methods for parameter estimation such as Estimation of Signal Parameter via Rotational Invariance Techniques (ESPRIT) and Matrix Pencil technique are deployed to extract the mode information. The investigation reveals the superiority of the Matrix Pencil method over the ESPRIT method for inertia estimation application. Once the mode information is available, an equivalent swing equation is used to estimate the inertia at any desired bus of the power system. The analysis is carried out on both Kundur's two-Area system and the IEEE-39 bus system. The results obtained demonstrate the superiority of Matrix Pencil based method over ESPRIT method for inertia estimation application. © 2021 IEEE.