If there is a particular version on YouTube with this title, it might be special because of the way it's performed. Maybe it has a unique musical arrangement, or the singer has a very soulful voice that brings out the meaning of the hymn in a special way. Also, the hymn itself is special as it tells of the old and important religious stories that are central to the faith of many.
I'm not familiar with a specific 'you tube hymn tell me the old old story' in a unique sense. But generally, 'Tell Me the Old, Old Story' is a hymn that has been passed down through generations, carrying religious and spiritual significance for many people.