To facilitate the green transformation of enterprises and realize low-carbon development, governments have adopted the policies of carbon emission constraint and carbon trade to promote enterprises’ low-carbon production. Although the two policies aim to reduce carbon emissions, they have different effects on enterprises’ production. Meanwhile, the development of remanufacturing caters to the low-carbon economy. Therefore, this article establishes the game models between an original equipment manufacturer (OEM) and a remanufacturer under carbon-emission-constraint and carbon-trade policies, analyzing the production decisions of enterprises under different policies to compare the influence of the two policies on outsourcing remanufacturing. The main conclusions of the article are as follows: (1) Both carbon-emission-constraint and carbon-trade policies increase the unit retail price of remanufactured and new products, reducing the new products sales volume. However, the sales volume of remanufactured products only decreases if the discount rate is less than the rate of carbon emissions of the two products. (2) The upper limit of carbon emissions can affect the unit outsourcing cost. The unit cost of outsourcing under the carbon-emission-constraint policy is only higher when the upper limit of carbon emissions is less than a certain threshold, and the discount rate is larger than the proportion of carbon emissions for both products; otherwise, the unit outsourcing cost under the carbon-trade policy is higher. (3) Both policies lessen the total environmental implication. When the upper limit of carbon emissions is less than a particular threshold, the environmental effect of the two manufacturers under the carbon-emission-constraint policy is smaller; otherwise, the environmental impact is smaller under the carbon-trade policy.