From a pure functional perspective, the 2 page system sometimes allows for home realm discovery (where the user has accounts in more than one system)
For example, Microsoft has something called the Microsoft Account and the Organizational Account. The username feature allows HRD to redirect to the correct authenticating server. This feature is live and active for all Azure, O365, and related sites.
LiveID, or Passport is now known as the Microsoft Account
Azure Active Directory, Office 365, WAAD, and possibly ADFS all use "Organizational Accounts"
It is possible to have an account in the form of firstname.lastname@example.org at one or both directories. You can test for the presence of an account in one or the other directory by checking the JSON available here