Neither is reliable in absolute terms, but both are reliable in relative terms. They rely on different models (the Sustainable Web Design Model v4 for Website Carbon, an analysis of the page in the browser for EcoIndex) and on different scopes, which is why their results differ. Choose one tool, stick with it and track how your score changes over time: the trend is reliable, the absolute figure is not.
Read the source article: Website carbon footprint: how to calculate and reduce it