In an AC microgrid, the grid-supporting converter can operate either as a current source or a voltage source. By establishing the state-space models of parallel inverters for different operating modes, this paper conducts the stability assessment of droop-controlled grid-supporting inverters, and compares parallel inverters operating as voltage sources and current sources in AC MGs. Detailed analyses of participation factors, damping ratios, and oscillation frequencies are also performed for the given inverter operation. Furthermore, the effect of key control parameters on the system stability are analyzed. Finally, analytical results are further verified through simulation studies.