Supply chain carbon abatement is an important way to promote low-carbon transformation of the social economy and address global climate change. This paper analyzes the issue of supply chain carbon abatement under different power structures, as well as the effect of consumers’ low-carbon preference and carbon tax rate on the optimal decisions. This paper constructs five different models, namely ML-NO model, ML-CS model, RL-NO model, RL-CS model and VI model. The research finds that VI model is the most ideal model for promoting supply chain carbon abatement. The optimal abatement efforts, market demand, and total profits in the VI model are all the largest among the five models. Whether the supply chain leader is the manufacturer or the retailer, cost sharing contract can enhance optimal abatement efforts, market demand, and profits of both parties. In any model, the leader in Supply chain earns higher profits than the follower. When consumers’ low-carbon preference increases, the optimal abatement efforts, market demand, and profits of both parties will all increase, and the growth rate is gradually accelerating. For the manufacturer with high carbon emissions, when the carbon tax rate increases, the optimal abatement efforts first increase and then decrease. For the manufacturer with low carbon emissions, when the carbon tax rate increases, the optimal abatement efforts will also increase.