China has established a nationwide carbon quota trading market. Drawing upon international experiences and the strategic vision of the Chinese government, it is anticipated that China will soon incorporate a carbon tax system. The futurescape envisions a parallel progression of both the carbon market and the carbon tax system. This prompts an exploration into the circumstances where one should prioritize the carbon market system over the other, and vice versa. This paper constructs a repeated oligopoly game model to juxtapose equilibrium points under both carbon trading and tax regimes. Through rigorous analysis, it is discerned that under a duopoly with bounded rationality and inelastic pricing, if the carbon tax is set referencing the clearing price of the carbon market, then both the carbon trading and tax regimes can achieve identical emission reduction outcomes. Stemming from this revelation, for regions with established inelastic, oligopolistic carbon markets, it would be prudent to manage emission sources not included in the carbon market by setting a carbon tax in line with the market's clearing emission price. Furthermore, measures might be considered to dismantle such oligopolistic dominance to enhance emission reduction efficiency, or to transition from the carbon market to a tax regime for cost-efficient administration. For regions yet to embrace a carbon pricing mechanism, if there's an anticipation of forming an oligopolistic and inelastic carbon market, given the lower administrative costs, diminished enterprise operational risks, and broader coverage of the carbon tax regime, the region should gravitate towards the carbon tax system as a priority.