Microsoft Authenticator is a mobile app for two-step verification that replaces the older Microsoft Account app. Like Google Authenticator, the ideal way to add accounts to the app is by scanning QR codes with your mobile device's camera.
Not limited to Microsoft: While the old Microsoft Account app could only be used with your actual Microsoft user account, Microsoft Authenticator can be used with any account that offers a QR code or a secret key -- including Google.
Easy expiration view: The new app adds a numerical timer, so you know exactly how much time you have before your current authentication code expires and a new one is generated. Google Authenticator does not have this feature.
Clearer labeling: The old app didn't make it clear that you could use it to authenticate multiple Microsoft accounts. When you enter the Add Account screen in Microsoft Authenticator, you get one option labeled Personal Account and another labeled Work or School Account. This app gives all accounts a label, whereas Google Authenticator sometimes just lists an account according to the user name. Microsoft Authenticator's entries are also listed alphabetically for easier navigation, while Google's app appears to list entries according to how recently they were added.
Quick confirmation is limited to your Microsoft account: When you log in to a Microsoft account that is protected by this app's authentication, you will get a notification on your mobile device, and you can just tap to confirm or deny the login request. This is much handier than typing in a code, but unfortunately you cannot do the confirm/deny tap with non-Microsoft accounts; you must manually enter a code.
Microsoft Authenticator's numerical timer and sensible entry organization makes it more pleasant to use than the old app, and it can now be used for non-Microsoft accounts. These factors give it an edge over Google Authenticator, though some Android users may not be comfortable with relying on a Microsoft product for account security.