Synchronization of chaos, which was proposed by Pecora and Carroll, has a potential application for secure communications to generate chaotic carrier. The methods to obtain synchronized chaotic oscillation in laser systems are classified into two categories : a master-slave-type; and a mutually-coupled-type. In a master-slave type the master and the slave laser are unidirectionally coupled, whereas in a mutually-coupled-type two chaotic lasers form a new composite cavity. So far, the difference in synchronization performance between these two types has not been well investigated. Moreover, to realize the synchronization in experiments, it is necessary to examine the conditions required for synchronization, particularly the range of allowed deviations from perfectly identical laser conditions for two lasers. In this paper, we numerically demonstrated the synchronization of chaos in two microchip solid-state lasers.