The parallel operation of power converters is essential to meet increased power demands. However, due to dynamic coupling, the instability in one converter can affect the stability of another. Therefore, this paper analyses the interaction and stability differences among the weak grid-tied photovoltaic (PV)-interfaced parallel voltage-and current-source converters (VSCs and CSCs) considering the PV generator (PVG) dynamics. Moreover, the impacts of the changing PVG operating points from the constant-voltage to a constant-current region (CVR to a CCR) and changing control parameters on converters' dynamic interaction are studied and compared in both cases. It is found that parallel VSCs dc-links suffer from low-frequency (<60 Hz) compared to high-frequency oscillations (>200 Hz) in parallel CSCs at the CCR with a short-circuit ratio (SCR) of 2.5. Moreover, the oscillation magnitude of injected power is higher in parallel VSCs compared to the parallel CSCs at SCR=1.2. Therefore, a stabilization method is proposed for both systems to ensure reduced interactions and stable operation in the CVR, CCR, and maximum power regions at weak and very weak grid conditions. Finally, the proposed compensators' efficacy is validated via detailed nonlinear time-domain and real-time simulation results.