Contemporary problems in process systems engineering often require model-based decision support tool. Among the various modelling paradigms, equation-based models and agent-based models are widely used to develop dynamic models of systems. Which is the most appropriate modelling paradigm for a supply chain? In this paper, we seek to address this important question through a well-structured benchmarking process. First, we demonstrate that in the space of models, ‘equations’ and ‘agents’ are concepts of a different order, the former referring to the system description elements in the model while the latter emphasises the model elements. Thus conceptually, the two paradigms are not mutually exclusive. Next, in a case study different dynamic models of an oil refinery supply chain are developed, using different tools and approaches. By performing detailed experiments with two different models, it is demonstrated that the models are equivalent when compared using model definition, numerical results and recommended decisions. However, the modelling process itself is different and results in different model structures. By analysing the effort required to expand the models, allowing new scenarios to be tested, and re-use of model components, we identify the strengths of the two paradigms in the context of supply chain modelling.