Terminology translation plays a critical role in domain-specific machine translation (MT). In this paper, we conduct a comparative qualitative evaluation on terminology translation in phrase-based statistical MT (PB-SMT) and neural MT (NMT) in two translation directions: English-to-Hindi and Hindi-to-English. For this, we select a 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 into consideration. We evaluate the MT systems’ performance on terminology translation, and demonstrate our findings, unraveling strengths, weaknesses, and similarities of PB-SMT and NMT in the area of term translation.