Nutraceuticals are an ever-expanding market worldwide, facing the unstoppable transition towards a green economy. Developing economically feasible and sustainable alternatives to current raw materials for the extraction of nutraceuticals is, therefore, essential to reach these goals and, at the same time, achieve social and economic competitiveness. This paper intends to propose an economical and environmentally sustainable feedstock for chlorogenic acid (CGA) and inulin, whose current extraction from green coffee and chicory, respectively, is unsustainable. Our approach is based on the multi-criteria decision-making approach (MCDA), supported by the analytical hierarchy process (AHP), ranking the performance of competitor biomasses according to economic, social, and technological criteria. The results of this study highlight cardoon (Cynara cardunculus) as a promising raw material for the extraction of CGA and inulin in virtue of the high concentration, low-input growth regime, and the possibility of being grown on marginal lands. Nevertheless, cardoon biomass availability is currently scarce, extraction methods are underdeveloped, and consequently, the obtained product’s price is higher than the benchmark competitors. Policies and investments favoring sustainable cultivations could stimulate cardoon employment, linking economic advantages and land requalification while limiting phenomena such as desertification and food competition in the Mediterranean basin.