To regulate the development of the electric vehicle battery recycling industry, many governments, including China, have proposed the extended producer responsibility (EPR) system, which emphasizes that producers are responsible for the entire life cycle of their own products, especially the recycling of discarded products. As compliance schemes of the EPR system, collective producer responsibility and individual producer responsibility (CPR and IPR, respectively) systems received varying degrees of preference. In this paper, we consider two vehicle producers with a competition-cooperation relationship and investigate the implications of scheme adoption on recycling technology investment. The two vehicle producers compete in the forward supply chain and cooperate in the reverse supply chain under the CPR system. Specifically, the two competing vehicle producers invest in recycling technology separately under the IPR system but negotiate it under the CPR system, and we use the Nash bargaining game model to characterize the negotiation between them. The key findings are as follows: When the recycling-technology-investment effectiveness is relatively low, or the investment effectiveness is high and the brand differentiation between vehicle producers is significant, they reap higher economic benefits under the collective recycling system. In addition, only when the investment effectiveness is relatively high and the brand differentiation is insignificant will environmental benefits (reflected by the recycling technology level) be higher under the collective recycling system. Furthermore, consumers’ preferences for recycling systems are always consistent with those of vehicle producers. Interestingly, when the investment effectiveness is relatively high, under moderate brand differentiation conditions, Pareto improvements in economic benefits, environmental benefits, and consumer surplus can be achieved simultaneously under the collective recycling system, i.e., the two competing vehicle producers can maximize overall social welfare through win-win cooperation.