In this paper, we investigate the strategic decisions of the greening level in a competing supply chain framework where consumers have explicit preferences for green products. We consider a three-stage game-theoretic model where manufacturers' greening decisions, which are long-term in nature, precede their wholesale price decisions. In the final stage, the retailers either compete in price (Bertrand) or quantity (Cournot). The greening decisions before wholesale price decisions in the presence of consumers' preference for environmentally friendly products lead to insightful results. Our paper shows the optimal greening level in the Bertrand competition is higher than in the Cournot competition. Despite higher greening cost involvement in Bertrand competition, the manufacturer charges a lower wholesale price and produces a higher quantity than the Cournot competition. Comparing profits between Cournot and Bertrand models reveals that Bertrand equilibrium yields higher profit than Cournot equilibrium when competition is moderate, unlike the conventional results that Bertrand firms get zero economic profit. Our paper implies that the greening aspect of a product works as a differentiating strategy when the competition is not intense. The differentiating strategy leads to higher greening levels, which reduces the per-unit carbon emission levels. At the same time, consumers' preference for green products jacks up the demand, leading to the demand effect. Therefore, a higher greening level of a product can lead to a higher demand effect, which crowds out the greening benefits at the aggregate level. Hence, it is unclear which models-Bertrand or Cournot-are more efficient in improving the environment. We show that the Bertrand model's overall environmental impact is lower if the initial carbon emission is below a threshold. Our results imply that the regulators should create environmental awareness among consumers, which will put pressure on the manufacturers to undertake higher greening activities rather than only framing policies to promote direct competition among firms. Since consumers' greening sensitivity yields a higher greening level only in price competition if the initial carbon emission level is lower, the regulators can promote price competition by introducing higher carbon taxation in the industries where initial emission levels are higher to enhance the greenness level of the products and further improve the environment.