Arun Sirpal explains some of the security features exposed in Azure SQL Database:
You do not really have to use all of them, this is down to you and your requirements but at least you have decisions to make. I will mention TDE (Transparent Data Encryption), I know a lot of people will opt for TDE in Azure. The big advantage of TDE in Azure over the earthed flavour is that Microsoft does a lot of the work for you, especially around the key management side of things. Also assuming your database is in a geo-replication partnership it will be protected by a different key on each of the servers. Microsoft will also rotate your certificate at least every 90 days, doing this with a local based SQL Server can be quite manual and fiddly (well I think it is).
Read the whole thing if you’re thinking of moving forward with Azure SQL Database, or if you already have a database up in Azure and haven’t checked the latest offerings yet.