Manufacturers now-a-days are interested in selling remanufactured products in order to promote sustainability. In this paper, we study the impact that the brand of a remanufactured product has on total profit. To that end, we consider closed-loop supply chain consisting of a single high-brand manufacturer, a single low-brand manufacturer and a single retailer. The high-brand and low-brand (re)manufactured products are produced by the original equipment manufacturer and both the products are assumed to be sold exclusively through a retailer. Mathematical models are developed considering price competition and integration between high-brand and low-brand manufacturers. We have shown that the integration of a retailer with a manufacturer of high-brand products generates more profit compared with the integration of a manufacturer of low-brand products with a retailer. We have also conducted a numerical study to analyse the effect of market size and cross-price elasticity on total supply chain profit. The results suggest that brand effort level is higher for an integrated system compared with that for a decentralised system.