Final answer:
Use Azure Import/Export service for transferring large amounts of data over suboptimal network conditions and when data size doesn't justify a Data Box. Data Box Family is best suited for petabyte-scale or highly secure offline data transfers.
Step-by-step explanation:
The Azure Import/Export service should be used when transferring large amounts of data to and from Azure when network conditions are suboptimal, such as when you have limited bandwidth or a non-reliable connection. Situations may include moving terabytes of data, which would take a prohibitively long time over a standard internet connection. On the other hand, the Data Box Family is suitable when dealing with larger datasets (in the petabyte range) or when you require a more secure and robust offline data transfer solution. Data Box devices have built-in security features that help with protecting your data during transit.
Typically, if your data transfer needs exceed the capability of your network infrastructure but aren't large enough to require a physical Data Box, the Import/Export service would be the appropriate choice. However, for mass data migrations and especially secure transfers, the Data Box family of products would be recommended.