Unsteady flow physics of two types of vertical axis wind turbines (VAWTs), namely, a modified Savonius turbine and a hybrid Darrieus-modified-Savonius (HDMS) turbine, are numerically studied using a fluid-structure interaction approach. As a first step, a numerical solver is developed by coupling the wind turbine dynamics with a high-fidelity flow solver, thus, synchronizing the flow-turbine interaction. The solver is then used to study unsteady aerodynamics of wind-driven modified Savonius and HDMS VAWTs under different loading conditions. The relationship between the power efficiency and tip speed ratio (TSR) is invested for both types of wind turbines. It is found that there exists large disparity on energy harvesting performance between the two types of VAWTs under wind-driven flow conditions. The modified Savonius VAWT achieves relatively high power efficiency (~30% or ~51% of the Betz's limit) at small TSRs; the HDMS VAWT achieves high power efficiency (~40% or ~67% of the Betz's limit) at large TSRs. At the same incoming wind speed, the maximum power efficiency of the HDMS VAWT is about 10% higher than that of the Savonius VAWT. It is also observed that the external loading can affect dynamic stall over Darrieus blades of the HDMS VAWT, thus significantly varying the TSR and the corresponding energy harvesting efficiency.