Two key issues are at the core of the current research on international trade: bilateral flow intensity estimations and link prediction. This study proposes a fair and detailed comparison (using exactly the same input data) of the performances of two consolidated tools, the Gravity Model (GM) and the RAS algorithm. The main novelty is the application of these methodologies to reconstruct the network architecture with a minimum amount of information (national import and export). Moreover, we implement a multi-layer analysis to provide a comprehensive and robust framework. Our methodological approach is tested over several food commodities, over the period 1986-2013. The main outcomes suggest that the RAS algorithm outperforms the Gravity model in the estimations of the bilateral trade flows, importantly guaranteeing the balance constraints (i.e., global import equals global export), while GM generates lower relative errors, but it underestimates total global flows. Both RAS and GM can be applied to accurately recover the network architecture. The implications of our study encompass a wide range of applications, such as: systemic-risk assessment in the international trade system, creation of new databases, and scenario analyses to support policy discussions and decisions.