This is an excellent question. Full disclosure as I am partial to Azure but have experience with the others.
Where I think Azure stands out from the others is the quick transition from on prem to the cloud. For example -
- SQL Azure - change connection string, upload DB, go!
- Queues work a lot like MSMQ.
- Blobs are pretty much blobs any way you shake them but they scale like crazy.
- The table storage component is good because it provides incredible scalability for name/value pairs - but takes some getting used to.
- Service Bus is my favorite of the services because it allows for a variety of communications paradigms. Two SB endpoints first try to connect to each other, if they cannot, then they route through the cloud - makes for very secure and scalable processing when firewalls tend to get in the way.
- Access control list - paired typically with the service bus to make sure the right people access the right things - think SAML in the cloud.
I hope that helps!