I recently updated an application from Entity Framework 5 to version 6. MSDN provides some instructions.
The upgrade required a couple of code changes for me.
1) I received a compilation error:
“The Entity Framework provider type ‘System.Data.Entity.SqlServer.SqlProviderServices, EntityFramework.SqlServer’ registered in the application config file for the ADO.NET provider with invariant name ‘System.Data.SqlClient’ could not be loaded. Make sure that the assembly-qualified name is used and that the assembly is available to the running application.”

To resolve, I needed to add code to my class that inherited from DbContext:

public class MainContext : DbContext 
		static MainContext()
            // Include this line to register the SQL Provider with Entity Framework 6
            var dummy = typeof(System.Data.Entity.SqlServer.SqlProviderServices);

2) ‘EntityState’ was moved to a different namespace, so I needed to add a ‘using’:

using System.Data.Entity;

to accommodate the change:
System.Data.EntityState => System.Data.Entity.EntityState

One benefit in EF 6 was being able to access and log the SQL generated by an EF statement. I added code to my override of DbContext.Save.

var commandText = new StringWriter();
this.Database.Log = s => commandText.Write(s);