With the rapid development of electric vehicles (EVs), many EV batteries have entered the retirement stage, leading to increasing concerns about the impact of resource recycling and environmental sustainability. Some countries have successfully applied reward–penalty and deposit–refund mechanisms in similar fields, such as lead-acid and waste portable batteries. However, whether these mechanisms are conducive to collecting waste EV batteries is unclear. This study aims to comprehensively analyze the influence of reward–penalty and deposit–refund mechanisms in EV battery collection by developing a Stackelberg game theoretical model. In the model, the recycling enterprise is the leader and the EV manufacturer is the follower. Furthermore, the total social welfare is used as the indicator to select the optimal incentive mechanisms. The results show that (1) both mechanisms could improve collection rates and recycling enterprises’ profits, though the collection rate is lower under the reward–penalty mechanism than the deposit–refund mechanism unless the reward/penalty coefficient takes a very high value. (2) Regardless of government focus on increasing the sales volume of new EV batteries, collection rates, or social welfare, the boundary conditions of the choice of the two mechanisms are obtained. Additionally, the boundary conditions are related to the trade-in discount and refund coefficient. (3) Under the deposit–refund mechanism, even if the refund coefficient is less than 1, the mechanism may still lead to a higher collection rate than the reward–penalty mechanism.