Inside the readme file of the ASP.NET Universal providers NuGet package is this quote
The SqlMembershipProvider, SqlRoleProvider, SqlProfileProvider classes that shipped in ASP.NET through version 4 support only Microsoft SQL Server and Microsoft SQL Server Express. They do not support newer offerings such as Microsoft SQL Azure and Microsoft SQL Server Compact.
However, when I run the custom aspnet_regsql scripts for Sql Azure http://support.microsoft.com/kb/2006191 and then point my web.config to the SQL Azure database, ASP.NET membership seems to work correctly.
Can anyone tell me what exactly doesn't work with SQL Azure, that the universal providers enable?