As found in the MUI files of the WP8.1 emulator, the phone will now back up not just your apps, but also contents like high scores, notes, and settings to OneDrive. Of note is that developers need to enable this feature, seemingly only formalizing what some developers were doing already.
New in Windows Phone 8.1 is that the OS will now also back up your Start screen layout, and also browser details such as passwords.
SMS messages are of course already backed-up, but the OS will now give you a choice of how far back in the past you want to restore.
Overall it seems restoring a phone will be a much better experience in Windows Phone 8.1 than Windows Phone 8.