Luckily, Backuptrans iTunes Backup Extractor is a good option to open your previous iTunes backup and to restore data from iTunes Backup back to your iPhone or iPad correctly. With Backuptrans iTunes Backup Extractor, you can recover and restore valuable data (e.g. SMS messages, Contacts, Videos, Photos, Calendar events, Recordings, Voicemails, Notes, Bookmarks and other app data)from iTunes Backup back to your iPhone or iPad with iOS 7. Restoring data from encrypted iTunes backup is also supported. If you are using Mac, jsut download iTunes Backup Extractor for Mac to use.
The data restoring process is simple. Run this iTunes Backup Extractor program on your computer and then load data from your iTunes Backup files. You can view all the backup data including SMS messages, Contacts, Videos, Photos, Calendar events, Recordings, Voicemails, Notes, Bookmarks and other app data etc. Now just connect your iPhone or iPad to computer via usb and then click the "Restore to Device" button. See the detail tutorial on how to restore data from iTunes Backup after updating to iOS 7 step by step.
If you need to revert back to iOS 6, iTunes Backup Extractor even makes it possible to restore data from iOS 7 iTunes backup to a downgraded iOS 6 device.
Contact me if you have any question.