Unmanned aerial vehicles (UAVs) can be harnessed as relay nodes in free-space optical (FSO) communication systems to realize a flexible and cost-effective approach for delivering on-demand communication in next-generation wireless communications. However, fading channels can adversely affect the performance of UAV-assisted dual-hop FSO systems owing to various factors. This paper presents a unified system performance analysis of UAV-assisted dual-hop FSO/FSO systems with the amplify-and-forward relaying protocol and intensity modulation/direct detection technique. For general applicability, the influence of the attenuation loss, atmospheric turbulence, pointing error impairments, and angle-of-arrival (AOA) fluctuations on the FSO link between the source and the UAV is considered. Meanwhile, the FSO link between the UAV and the destination is modeled using Málaga distribution channels, which are affected by atmospheric turbulence. The tight closed-form expressions for the outage probability and the average bit error rate of the dual-hop system are derived, followed with the diversity order of the system in the high signal-to-noise ratio range. Furthermore, the impact of various system parameters and channel parameters correlated with the attenuation loss, atmospheric turbulence, pointing error impairments, and AOA fluctuations on the system performance is studied, and a detailed comparative investigation of the various modulation schemes is conducted. Finally, simulation results are presented to validate the analytical results.