This study addresses a comparative analysis of carbon emissions policies and optimal decisions in competitive closed-loop supply chains. It examines three policy scenarios: a single carbon tax, a single cap-and-trade, and a mixed policy. Competitive intensity, the degree of competition among manufacturers, and product recycling rate, a key element in closed-loop supply chains, can impact the comparative analysis of carbon policies and optimal decisions in competitive closed-loop supply chains. A supply chain system is constructed, consisting of two manufacturers and a shared retailer. We employ a decentralized decision-making approach, with a Cournot game between the manufacturers and a Stackelberg game with the retailer. The analysis considers the impacts of carbon tax, carbon trading price, and recycling rate on optimal decisions and total supply chain profit. The results demonstrate that the mixed carbon policy can yield superior economic and environmental benefits compared with the single carbon tax policy. Mixed policies are likely to be relatively less profitable in most cases than a single cap-and-trade policy. Notably, when the mixed carbon quota exceeds a certain threshold, the mixed policy surpasses the single cap-and-trade policy both economically and environmentally. This study extends previous research by examining the impacts of the recycling rate and various carbon policies on supply chain decisions and profit. The findings offer insights into optimal strategies for reducing supply chain carbon emissions, which benefits policymakers and managers. Finally, it suggests that enterprises should consider a mixed carbon policy to balance economic and environmental goals.