Analyzing the logistics management performance of road and rail freight transport is essential to improving overall visibility along the supply chain. In this paper, data envelopment analysis (DEA) and the multicriteria decision-making (MCDM) method, using the analytic hierarchy process (AHP), were integrated to assess the logistics management performance of road and rail freight transportation from a sustainability perspective. First, a global review of the integration of DEA and MCDM was conducted to evaluate the sustainability of logistics performance in road and rail freight transportation, covering the period from 2010 to 2023 using the Scopus database. A survey was then conducted, and the AHP technique was used to determine the weight of different criteria, representing all three sustainability parameters, namely environmental, social, and economic, that impact the logistics management performance of the freight transportation process. In addition, the efficiency score for both transport modes was calculated using the DEA tool. Finally, a real-world case of road and rail freight transport in Hungarian industries was considered to assess logistics management performance efficiency. The findings show that companies prioritize economic factors over social and environmental impacts. However, transportation policies support reducing social and environmental impacts for a more sustainable logistics sector. Therefore, decision-makers must work more efficiently to raise awareness of the sustainable logistics performance of the freight transport sector.