In reality most serious providers of translation services fall somewhere in between
the two in as much as they mediate resources but also provide added value through project management, document engineering and additional quality control. For the sake of practicality we refer to both as translation agencies.
It is unrealistic for an agency to have resources for checking every translation that it handles particularly since translation is such a cost-led business. Thus the responsibility for translation quality control usually lies with the translator unless agreed otherwise even though the agency is responsible directly to its customers for the quality of the deliverables. The purpose for which the translation is made will determine the level of quality control. In extreme cases a back translation is made into the source language is to compare this with the original text but this is usually prohibitive in terms of time and cost. It would be netter to ensure that an appropriate translator with the right skills is engaged from the outset.