The stability domains of the one- and two-polarization eigenstates operation regimes in lasers with controlled anisotropies are shown to be governed by the relative values of the linear phase and loss anisotropies. These domains are predicted theoretically in the case of the He-Ne laser when an internal parameter like the frequency is varied and experimental observations using the helicoidal eigenstates show very good agreement with the predictions. This study allows us to analyze the experimental results obtained as well in the case of very small lasers, i.e., semiconductor lasers when the injection current is scanned, as in the case of very large lasers, i.e., CO2 lasers with different cavity geometries.