Google search is worthless for the above comparison. Hence I made one myself after doing little research.
Azure is a cloud computing Platform and Infrastructure for deploying and managing applications and services through “Microsoft Managed Datacenters”.
For example, you can host websites or run couple of VMs at Microsoft Datacenter and you can access them remotely. The advantage is no upfront Datacenter or hardware cost. You just pay for the service and you don’t need to worry about Hardware upgradation cost. Disadvantage is you are going to store your “data” into Microsoft’s Datacenter and it is accessible to American Government. So it is questionable for storing sensitive data there.
At the moment, there are 24 datacenters world wide and Microsoft stores your “information” there and are accessible to American Govt if they want to. Confusingly Microsoft states they have privacy rules which complies with Europe’s privacy rules.
While Hyper-V is similar (or competitor) to VMware Vsphere. You can build VMs out of it similar to Vsphere.