Reasonable configuration of energy storage equipment could solve the mismatch problem between load demand and renewable power output. The energy storage devices could be classified into short-duration and long-duration storage according to the operation timescale. Short- and long-duration cooperative energy storage is a promising trend because of its complementary advantages. This work focuses on the systems of photovoltaics and wind farms combined with energy storage components, such as batteries, thermal energy storage (TES), and hydrogen energy storage (HS). The optimal design parameters are obtained by multi-objective optimization with the objective of levelized cost of energy and loss of power supply probability. The techno-economic performance of different short- and long-term cooperative energy storage systems are compared. The influence of rule-based strategies on the system performance is investigated. Results indicate that the system with batteries and TES has great competitiveness from an economic perspective, and the system with batteries and HS has a lower potential energy waste probability when the power-supply reliability is extremely high. The recommended discharging priority of the system with batteries and TES is TES first and then batteries, which could completely achieve power supply reliability.