Green hydrogen has been promoted as a vector for the global energy transition, especially in countries with high availability of renewable energy sources. In this context, Brazil has been consolidating itself as a destination for major investments aimed primarily at the production of green hydrogen and ammonia for export, driven by its vast renewable potential, port infrastructure, resources, and favorable geographical position. However, analyses that critically evaluate this strategy from the perspective of the rational use of energy quality are still scarce. This study evaluates the thermodynamic efficiency of the green hydrogen production chain, comparing the export strategy, domestic use of hydrogen, and the direct use of electricity within the Brazilian National Interconnected System (SIN). The methodology is based on exergetic analysis and the calculation of the Energy Return on Investment (EROI), considering the entire production chain of a plant with a capacity of 1,000 tons of green ammonia per day. The system analyzed consists of seawater desalination via reverse osmosis, SOEC electrolysis for hydrogen production, cryogenic air separation to obtain nitrogen, Haber–Bosch synthesis for green ammonia production, maritime transport, and an offshore wind farm dedicated to electricity supply. Based on the results of the exergy efficiency and the overall EROI of the ammonia export chain, it is observed that the process consumes more energy than it delivers at the destination. In contrast, the direct use of offshore wind energy through the SIN presents higher exergetic efficiency and EROI than the export chain. When intended for domestic use, diesel in heavy-duty transport and mineral coal in heat generation, green hydrogen shows a greater thermodynamic advantage compared to other conventional energy vectors, as it allows the substitution of fossil fuels in specific applications with better utilization of the available energy quality. Therefore, although the export of green hydrogen is economically attractive, it results in significant exergetic losses. From the perspective of rational energy use, thermodynamics, and national energy security, prioritizing the domestic use of hydrogen or direct renewable electricity constitutes a more energetically favorable strategy. Thus, it is recommended that green hydrogen production prioritize non-dispatchable surplus energy and its use in domestic sectors, preserving exergy for national socioeconomic development.