The aim of this study was to highlight the interrelationship between the environmental, social, and economic pillars of agricultural sustainability and their impact on rural development in EU countries. By considering the cumulative influence of 15 social, economic, and environmental indicators, the study clustered the EU countries into five homogeneous groups using principal component analysis and cluster analysis. The research findings confirm that there is a significant trade-off between the three dimensions of sustainability, particularly between the environmental dimension, on the one hand, and the socio–economic dimension, on the other. Thus, the main real challenges identified for the countries included in cluster 5 (Bulgaria, Greece, Croatia, Lithuania, Latvia, Poland, Romania, and Hungary) are related to the socio–economic pillar of sustainability. Moreover, for four EU countries (Netherlands, Belgium, Denmark, and Ireland), included in two different clusters, achieving environmental goals such as reducing agricultural emissions (SDG 2.60) and increasing area under organic farming (SDG 2.40) represents a significant issue in sustainable agriculture. The results highlighted specific challenges to sustainability in agriculture for EU countries that can hinder its effects on rural development. Therefore, tailored measures should be designed to efficiently address these specific issues.