If you go with the Azure website approach, you will run into issues if you try using Azure Storage for the "external file system". It was able to create the container, but unable to write files inside it. I wasn't able to resolve it; but, I believe it is related to the directories where Kentico saves the temporary files - Azure websites don't have C:\ and the web.config override settings didn't seem to make a difference (setting it to a writable path).
No issues at all when using a Cloud Service.