The streamflow process is an crucial information resource for the joint optimal operation of reservoirs. As the length and representativeness of historical streamflow samples are insufficient for practice projects, streamflow stochastic generation approaches are usually used to expand the streamflow series. For the joint operation and management of the multi-reservoir system, the multisite streamflow stochastic generation (MSSG) with high-dimensional temporal-spatial correlation poses a challenge. This paper develops the generative adversarial network as a novel MSSG model. In contrast to the existing literature on MSSG, which solely focuses on a specific case study and provides a comparatively one-sided assessment, this paper evaluates multiple characteristics of streamflow at various time scales from three MSSG models in two instances. Specifically, three MSSG models, namely the seasonal autoregression (SAR) model coupled with the master station method, the Copula model coupled with the master station method, and the deep convolutions generative adversarial network (DCGAN) model, are employed to generate monthly, ten-daily, and daily streamflow series of the two-reservoir and eight-reservoir systems. This study aims to examine the performance of three models and provide recommendations for implementing MSSG approaches in practice. Results show that: (1) the priority should be given to the maximum iterations on the DCGAN model at a large time scale, while at a smaller time scale, the training of the model is directly linked to the setting of batch size; (2) the Copula model is capable for better retaining statistical characteristics of streamflow series for similarity; (3) the SAR model excels in simulating the extremes of streamflow; and (4) the DCGAN model possesses a significant advantage in capturing the temporal-spatial higher-order correlation, especially in systems comprising more than two reservoirs and with small time scales (e.g., daily streamflow). Furthermore, this study presents comprehensive and multi-scale recommendations for selecting MSSG approaches, thereby providing a theoretical foundation and practical value for MSSG in diverse scenarios.