iTunes backup isn't restoring all content

I got an iPhone 6s today, so I backed up my old iPhone (iPhone 6) onto iTunes and then restored that backup onto my new phone. It restored my contacts and my music, but no settings, photos, or apps transferred over. I encrypted my backup, deleted my backups and retried the whole process...nothing will work! I tried using iCloud but I don't have enough storage space to backup all of my stuff and I would really rather not pay for more storage space.

Please help!