Many of the solutions we have created for our organization have been released as Python based Geoprocessing Tools (sometimes rolled-up into widgets, other times simply a GP Service).
Since we've implemented a (federated) Enterprise system, we've been exploring leveraging the Python API much more.
As I see it, the primary difference here is that the GP services can access the underlying geodatabase infrastructure directly. Conversely, the Python API is designed to be web-based and would therefore access the data via feature services.
I realize this is the Python API forum/group so this may need to be posted elsewhere to get a good discussion going.
That said, what do you see as the advantages to using the Python API vs 'conventional' geoprocessing tools? Are there performance considerations? Ease of deployment?