Q: Why would I ever install SQL Server on a Windows Azure IaaS virtual machine if SQL Azure were available?
A: With Windows Azure IaaS, you install the operating system onto a virtual machine, and your application can then do whatever you want as long as you stay within the rules for Windows Azure IaaS (e.g., don't try to configure a static IP address or use multicast traffic). This means you can install SQL Server on a virtual machine and have the full range of SQL functionality.
The SQL Azure implementation that's now called Windows Azure SQL Database provides a Database as a Service (DBaaS) offering based on SQL Server. However, the full range of SQL functionality isn't available because it's a shared offering. Although it's a great fit for numerous scenarios that require fairly generic database services, you can't customize several aspects. In addition, there are data size limitations—which is where using a standard SQL installation running in Windows Azure IaaS is a better fit. Windows Azure SQL Database doesn't support SQL Server Analysis Services (SSAS), SQL Server Replication Services (SSRS), or Service Broker, and only a subset of T-SQL is available.
The Microsoft Azure SQL Database page explains the capabilities of Windows Azure SQL Database. Microsoft TechNet provides a great comparison of Windows Azure SQL Database to SQL Server.