We systematically study the leader-laggard synchronization of polarization chaos in mutually coupled free-running vertical cavity surface emitting semiconductor lasers in two cases of parallel and orthogonal injection. Specifically, we quantitatively investigate the effect of critical external parameter mismatch such as the coupling intensity and frequency detuning on the leader-laggard relationship utilizing the cross-correlation function. When the difference between two main cross-correlation peak values exceeds 0.1, the leader-laggard relationship can be viewed to be stable. Our results demonstrate that compared with the coupling strength, the frequency detuning is the dominant factor in determining the stability of the leader-laggard relationship. The exchange of the leader-laggard role occurs within a frequency detuning region from -5 GHz to 5 GHz for both parallel and orthogonal injection. Once the leader-laggard relationship is stable, the difference between the two cross-correlation values can reach 0.242 for negative frequency detuning, but the corresponding value is only 0.146 under positive frequency detuning.