With the deepening of the green energy transformation, the power system presents the "double high" characteristics of a high proportion of renewable energy and a high proportion of power electronic equipment, and many new stability problems are highlighted. The traditional grid-based inverter control has the disadvantage of low inertia or even no inertia, and large-scale access will reduce the inertia of the power system, so it is necessary to cooperate with the grid-based inverter control to improve the stability of the system. Therefore, it is of great significance to study the parallel model of grid-forming control inverters and grid-following control inverters for the development of new energy. Virtual synchronous machine (VSG) control is more suitable for high proportion power generation system than other grid-forming control strategies because of its good damping characteristics. As a kind of grid-following control strategy, PQ control has significant advantages in supporting grid voltage and frequency. In this paper, the Thevenin and Norton equivalent models of the grid-forming VSG-controlled inverter (VSG-CI) and the grid-following PQ-controlled inverter (PQ-CI) in islanded mode are established respectively, and their parallel impedance models are derived. Then, the three operating modes are compared and analyzed by using the stability criterion of the global admittance stability criterion. And the influence of inverter control loop parameters, line impedance and inverter coupling with different control strategies on the system stability is studied. Simulation analysis and experiment verify the correctness of the theoretical analysis in this paper.