Hi John / Raymond,
Great question! There are of course a lot of factors which can impact VHD disk speed, and these can certainly be amplified in a public cloud environment. Generally you’ll be using IaaS VMs where you are directly provisioning the VM from Azure, in which case you can pick the VM “size”: https://docs.microsoft.com/en-us/azure/virtual-machines/windows/sizes. One of the variables you can select are storage optimized VMs, which support high-throughput disks – they may even be faster than your local ones.

With you specific scenario, it looks like you want to use the cloud as a DR site, in which case you have to replicate the data of the VHD to the cloud, then bring that VM online when needed. The easiest way is using Azure Site Recovery: https://docs.microsoft.com/en-us/azure/site-recovery/site-recovery-overview

If you’re looking for a faster connection between your datacenter and Azure, check whether you ISP supports ExpressRoute: https://azure.microsoft.com/en-us/services/expressroute/
Thanks!
Symon