If you need to move data to Azure from on-prem, or between Azure data centers, I just stumbled across a great little tool from Microsoft Garage (which incidentally is a place as well as a program – its where that photo was taken when I was last there!).
The Fast Data Transfer tool squeezes as much throughput from the connection as possible, and has both a local and Azure based components – the Azure side uses VM’s running in the subscription so will carry a cost.
More details and the downloads can be found here: https://www.microsoft.com/en-us/garage/profiles/fast-data-transfer/