As the aviation industry embraces the carbon trading market, the competition between full-service carriers and low-cost carriers in ticket pricing is becoming more complicated and worth studying. To this end, we introduce carbon trading into game theoretical models under different market power structures and use real data from China Eastern Airlines and Spring Airlines on the route from Sanya to Shanghai to study this problem. This differs from the existing literature as empirical research is mainly used in this field. Our main results show that the disparity in market power (Stackelberg game) alleviates competition intensity under carbon trading and leads to higher equilibrium prices than in the Nash game model. Meanwhile, even when the two airlines have similar market power, Spring Airlines still has incentives to voluntarily act as a follower of China Eastern Airlines instead of maintaining equal market power with China Eastern Airlines. Under mild regulation, the uplift of carbon prices promotes higher equilibrium prices and supports larger profits. For the sake of consumer welfare, this suggests that the regulation department should impose stricter regulations and grant subsidies to motivate the airlines to mitigate emissions by introducing clean technologies.