I don't know about this one. I only know
Full Moon Wo Sagashite based on the work of Arina Tanemura, and the anime is... so-so. Maybe it is for younger girls, despite the life-threatening disease theme and other somewhat unexpected plot twists.
KKJ seems a bit like
Sailor Moon, for the "girl with superpowers" theme, and the reincarnation theme, and the hairstyle of the main character
But I'm not sure. From artworks it seems different, but artworks sometimes have not much in common with the animation.