Where does your believe comes from?
For my opinion, there are no particular "advantages" of the inverting configuration if compared with the non-inv. version.
In contrast, the input resistance of the non-inv. opamp configuration is much larger than that of the inverter.
However, in some cases a phase inversion is needed for stability reasons - for example in feedback loops that contain several blocks.
In this case, an inverting configuration is one possible solution.