Please correct my wrongs. From my reading on the topic so far, it appears to me that both, Azure Blob Storage and File Service offer the ability to store file(s) and folder(s) (I understand that blobs can store any binary object, but any serialized binary stream is just a file at the end of the day) in a hierarchical structure that mimics a file system.
Only the API to access them are slightly different in that the File Service allows you to query the source using Win32 File I/O like functions as well in addition to using the REST API.
Why would you choose one over another if you wanted your application to store some files owned by your application's users?
A few items for your question:
If you are developing a new application then leverage the native Azure API directly into Blob Storage.
If you are porting an existing application that needs to share files then use Azure File Service.
Note that there are a few SMB protocol features that Azure File Service doesn't support.