Azure File Service is targeted more to internal file handling. With internal I mean mounting a directory to a VM in the cloud or on-premises so it can be loaded in you back-end (SMB based protocol).
For sharing files with end-users (web or apps) it probably makes more sense to use blob storage as this simplifies downloading through a URL and securing download through Shared Access Signatures.
This post shares more details on the comparison (at the bottom): https://blogs.msdn.microsoft.com/windowsazurestorage/2014/05/12/introducing-microsoft-azure-file-service/