Innovative applications based on two-dimensional solids require cost-effective fabrication processes resulting in large areas of high quality materials. Chemical vapour deposition is among the most promising methods to fulfill these requirements. However, for 2D materials prepared in this way it is generally assumed that they are of inferior quality in comparison to the exfoliated 2D materials commonly used in basic research. In this work we challenge this assumption and aim to quantify the differences in quality for the prototypical transition metal dichalcogenide MoS$_2$. To this end single layers of MoS$_2$ prepared by different techniques (exfoliation, grown by different chemical vapor deposition methods, transfer techniques, and as vertical heterostructure with graphene) are studied by Raman and photoluminescence spectroscopy, complemented by atomic force microscopy. We demonstrate that as-prepared MoS$_2$, directly grown on SiO$_2$, differs from exfoliated MoS$_2$ in terms of higher photoluminescence, lower electron concentration, and increased strain. As soon as a water film is intercalated (e.g., by transfer) underneath the grown MoS$_2$, in particular the (opto-)electronic properties become practically identical to those of exfoliated MoS$_2$. A comparison of the two most common precursors shows that the growth with MoO$_3$ causes greater strain and/or defect density deviations than growth with ammonium heptamolybdate. As part of a heterostructure directly grown MoS$_2$ interacts much stronger with the substrate, and in this case an intercalated water film does not lead to the complete decoupling, which is typical for exfoliation or transfer. Our work shows that the supposedly poorer quality of grown 2D transition metal dichalcogenides is indeed a misconception.
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