Phrase-based statistical machine translation (PB-SMT) has been the dominant paradigm in machine translation (MT) research for more than two decades. Deep neural MT models have been producing state-of-the-art performance across many translation tasks for four to five years. To put it another way, neural MT (NMT) took the place of PB-SMT a few years back and currently represents the state-of-the-art in MT research. Translation to or from under-resourced languages has been historically seen as a challenging task. Despite producing state-of-the-art results in many translation tasks, NMT still poses many problems such as performing poorly for many low-resource language pairs mainly because of its learning task’s data-demanding nature. MT researchers have been trying to address this problem via various techniques, e.g., exploiting source- and/or target-side monolingual data for training, augmenting bilingual training data, and transfer learning. Despite some success, none of the present-day benchmarks have entirely overcome the problem of translation in low-resource scenarios for many languages. In this work, we investigate the performance of PB-SMT and NMT on two rarely tested under-resourced language pairs, English-to-Tamil and Hindi-to-Tamil, taking a specialised data domain into consideration. This paper demonstrates our findings and presents results showing the rankings of our MT systems produced via a social media-based human evaluation scheme.