The performance of equal gain combining reception at free-space optical communication systems is analytically studied and evaluated. We consider the case when the total received signal undergoes independent and not necessarily identically distributed channel fading, modeled by the versatile mixture-Gamma distribution. Also, the misalignment-induced fading due to the presence of pointing errors is jointly considered in the enclosed analysis. New closed-form expressions in terms of finite-sum series of the Meijer's G-function are derived regarding some key performance metrics of the considered system, namely, the scintillation index, outage probability, and average bit-error rate. Based on these results, some useful outcomes are manifested, such as the system diversity order, the crucial role of diversity branches, and the impact of composite channel fading/pointing error effect onto the system performance.