This study examines the comparative effectiveness of Carbon Pricing mechanisms, such as the Emissions Trading System (ETS) and carbon taxes, versus Green Finance initiatives in promoting carbon mitigation within the Eurozone. By analyzing the issuance and holding of various bonds, including Social Bonds, Green Bonds, Sustainability Bonds, and Sustainability-linked Bonds, the research evaluates which policy tool is more impactful in reducing carbon emissions. Utilizing Bayesian Additive Regression Trees (BART) for variable selection and Dynamic Linear Models (DLMs) to capture time-varying effects, the study finds that Green Finance (as a bond), particularly through Green Bonds, has a more consistent and significant influence on reducing carbon emissions compared to traditional carbon pricing mechanisms. The findings suggest that while carbon pricing tools often encounter limitations due to market dynamics and corporate behavioral responses, Green Finance aligns financial incentives with environmental goals, making it a more effective strategy for achieving substantial carbon mitigation. These results highlight the need for policymakers to prioritize and expand Green Finance initiatives to drive sustainable development in the Eurozone.