Tolkien used this world as his Primary World, then built a Secondary World of Faerie into it. He used what we all know as a foundation to draw us in, then showed us his vision of a fantasy world, complete with heroes, villains and extensive history, culture and landscape.
Rowling used the Primary World and added directly to it, rather than building another world into it. While compelling, HP's world does not have the attraction for me that Middle Earth does.
I choose Middle Earth every time.