This paper analyzes the stability impact of hybrid power- and voltage-based synchronization control (HSC) on grid-forming inverters, considering different reference-frame implementations of virtual-admittance-based current control (VA-CC). It is found that with synchronous reference (dq) frame VA-CC, the HSC tends to jeopardize the system stability in weak grids, yet such adverse effect can be avoided when the VA-CC is implemented in the stationary reference (αβ) frame. Further, the HSC can help to dampen system dynamics for both αβ- and dq-frame VA-CC in stiff grids. Experimental results confirm the theoretical findings.