One of the key measures to control environmental problem is to implement the appropriate environmental policies. This paper establishes the differential game between regulator and duopoly under emission standard and emission tax to analysis the impact on total emissions and social welfare based on the market-based policy and command-and-control policies respectively. By comparing the impact of the two environmental policies on total carbon emissions and social welfare, we find that market-based environmental policy is not entirely superior to command-andcontrol environmental policy when considering the difference of market structure and the dynamic change of carbon emissions. The total carbon emission trajectory under the carbon emission standards is smaller than that under the carbon tax policy when certain conditions are satisfied. Meanwhile, the carbon tax policy has higher social welfare, and the above optimal decision will converge to a stable state. Therefore, in the case of duopoly market, carbon emission standards can quickly achieve the purpose of controlling the pollution, which is conducive to solving the ecological environment problems. But at the same time, there is a lack of efficiency which leads to the decline of social welfare. The government needs to use environmental strategies comprehensively according to the realities.