Something to think about. The development paradigm in Windows Azure can be different from AWS. In AWS you are essentially renting a VM with SQL Server on it for the database side. All the normal stuff you do from SSMS locally works with AWS, except a few instance level items since you don't have complete control of the instance level stuff. You also don't have Windows Auth working.

The SQL Database in Azure has a different paradigm and may have more/less SQL Server features at any point in time. At some point I think it will be always ahead of the boxed product in all areas, but not right now.

Therefore, if you are using SQL Database and looking to move, you should consider code changes involved.

In moving the data, I suspect SSIS would be one way to do this. I think you can get a bacpac of your schema/data as well, but I'm not sure if that's better or worse. In terms of backups from Azure: http://msdn.microsoft.com/en-us/library/windowsazure/hh335292.aspx

Import side: http://msdn.microsoft.com/en-us/library/hh710052.aspx

My company (Red Gate), makes some tools that might help as well: http://cloudservices.red-gate.com/. Our SQL Compare and Data Compare tools could also work with limited data sets.