We numerically investigate the complex nonlinear dynamics for two independently coupled laser systems consisting of (i) mutually delay-coupled edge emitting diode lasers and (ii) injection-locked quantum nanostructures lasers. A comparative study in dependence on the dynamical role of ! parameter, which determine the phase-amplitude coupling of the optical field, in both the cases is probed. The variation of ! lead to conspicuous changes in the dynamics of both the systems, which are characterized and investigated as a function of optical injection strength " for the fixed coupled-cavity delay time #. Our analysis is based on the observation that the cross-correlation and bifurcation measures unveil the signature of enhancement of amplitude-death islands in which the coupled lasers mutually stay in stable phase-locked states. In addition, we provide a qualitative understanding of the physical mechanisms underlying the observed dynamical behavior and its dependence on !. The amplitude death and the existence of multiple amplitude death islands could be implemented for applications including diode lasers stabilization.