In the electric vehicle (EV) industry, extended producer responsibility (EPR) strategies raise two key issues: the allocation of recycling responsibilities between battery suppliers and EV manufacturers, and the choice between collective (CPR) and individual (IPR) recycling programs. This paper examines the economic and welfare implications of various EPR strategies and deposit-refund policy designs within two competing supply chains, each consisting of one battery supplier and one exclusive EV manufacturer. We analyze equilibrium behaviors under three chain-to-chain competition structures: a pure centralized structure, a pure decentralized structure with manufacturer-led recycling, and a pure decentralized structure with supplier-led recycling, under both IPR and CPR programs. The results show that, in both centralized and decentralized chain-to-chain competition, CPR improves supply chain efficiency when recycling benefits from economies of scale, while IPR is more effective when recycling experiences diseconomies of scale, regardless of responsibility allocation. In a pure decentralized structure, CPR with manufacturer-led recycling maximizes supply chain profits under economies of scale, whereas IPR with supplier-led recycling performs best under diseconomies of scale. Under CPR with pronounced diseconomies of scale, an ex-post tax with a lower deposit or an ex-post refund with a deposit-based deduction is preferable in cases such as decentralized competition with supplier-led recycling and centralized competition. In other cases, a standard deposit-refund policy is more suitable.