Terminology translation plays a critical role in domain-specific machine translation (MT). Phrase-based statistical MT (PB-SMT) has been the dominant approach to MT for the past 30 years, both in academia and industry. Neural MT (NMT), an end-to-end learning approach to MT, is steadily taking the place of PB-SMT. In this paper, we conduct comparative qualitative evaluation and comprehensive error analysis on terminology translation in PB-SMT and NMT in two translation directions: English-to-Hindi and Hindi-to-English. To the best of our knowledge, there is no gold standard available for evaluating terminology translation quality in MT. For this reason we select an evaluation test set from a legal domain corpus and create a gold standard for evaluating terminology translation in MT. We also propose an error typology taking the terminology translation errors in MT into consideration. We translate sentences of the test set with our MT systems and terminology translations are manually classified as per the error typology. We evaluate the MT system’s performance on terminology translation, and demonstrate our findings, unraveling strengths, weaknesses, and similarities of PB-SMT and NMT in the area of term translation.