Tachibana Riku is an orphan who lives with his adoptive grandfather. Other than school and homework, Riku has to put up with lessons from his grandfather, teaching him seemingly meaningless hand signals and signs; meaningless, that is, until Riku is violently introduced to the world of 'shikigamis', fighting beasts with human owners. After witnessing his grandfather defend against a shikigami assault on their home shrine, Riku obtains his own Drive device to summon his own shikigami, Kogenta, and it turns out the hand signals give the shikigamis special powers. With his newly obtained powers, and a shikigami as a companion and friend, what adventures await Tachibana Riku? Do his powers have any relation to his parents' disappearance?
In the beginning God created the light and the dark, but soon, the powers of light squared off against the powers of dark, and the world was plunged into war. Eventually, seven knights of lights with the power of Shadow rose up and sealed the darkness away. Now, many years later, Nene, the ruler of the Grand Kingdom, is trying to use the power of Shadow to plunge the world into chaos. Looking for other people with the power of Shadow, Nene sends his forces to attack Shu's village; but while defending his village, Shu unleashes the Shadow of Blue Dragon, the most powerful shadow known, and it goes berserk. Can Zola and Jiro, two other Shadow users who oppose Nene, teach Shu how to control Blue Dragon and save the world from chaos?
Onmyou Taisenki and Blue Dragon although not related, have the same summon and fight backgrounds throughout the series.
In OT - Humans have devices which call beasts to fight for them, and the beasts are in relation to that persons personality along with their lament ability to use symbol gestures they later learn to grow.
In BD - By consuming a magical orb, humans have the power to cast their own shadows into magical dragons which fight battles for them as well, these dragons being summons of the persons inner and dwelling powers and strengths.
If you enjoy people that use summons that relate to themselves for fighting battles, this is a "both ways" recommendation.
Sumimura Yoshimori is a Kekkaishi – an inheritor of the power to battle demons, using barriers called kekkai. His family is charged with protecting the grounds of Karasumori high school, a building which magnifies the power of demons who enter it. Helping him are his spirit-wolf companion Madarao, and next door-neighbor Yukimura Tokine, the daughter of a rival clan. Years ago, Tokine was injured protecting Yoshimori, and now he is determined to become strong enough to keep her from being hurt again. Of course, he'd rather bake his exquisite cakes than have to fight demons at all, but fate has something else in store! As a shadowy demon organization moves to steal Karasumori's power, can Yoshimori overcome legions of demons, a centuries-old family rivalry, and a grandfather who just can't understand his love for baking?
Ever since Yugi Mutou completed the Millennium Puzzle his life has changed; he's made friends, learned how to play the card game Duel Monsters and has gained more confidence in himself. After his grandfather is beaten in a duel he is challenged by Seto Kaiba, ranked number two in the world, but Yugi beats him regardless. Now, as a result of his victory, Yugi has attracted the attention of the game's creator, Pegasus. Yugi is then challenged to a dual in an alternate reality where magic brings the monsters to life, but is beaten and his grandfather's soul is taken. In order to retrieve it Yugi must now participate in a tournament against the best duelists in the world, defeat the game's creator, and learn more about the secrets within his Millennium Puzzle!
If you like one, you will like the other.
They also share the same kind of feel to the main villain, being some kind of huge evil corporation. And the fact that they utilize "monsters" to do battle.