This paper reports on a comparative evaluation of phrase-based statistical machine translation (PBSMT) and neural machine translation (NMT) for four language pairs, using the PET interface to compare educational domain output from both systems using a variety of metrics, including automatic evaluation as well as human rankings of adequacy and fluency, error-type markup, and post-editing (technical and temporal) effort, performed by professional translators. Our results show a preference for NMT in side-by-side ranking for all language pairs, texts, and segment lengths. In addition, perceived fluency is improved and annotated errors are fewer in the NMT output. Results are mixed for perceived adequacy and for errors of omission, addition, and mistranslation. Despite far fewer segments requiring post-editing, document-level post-editing performance was not found to have significantly improved in NMT compared to PBSMT. This evaluation was conducted as part of the TraMOOC project, which aims to create a replicable semi-automated methodology for high-quality machine translation of educational data.