In the wake of a rebellion that shook Japan twenty years prior, Togame Hida, general director and strategist for the army, seeks to obtain the 12 "deviant blades" created by master swordsmith Shikizaki Kiki to help add stability and security to the Bakufu government. To aid in this endeavor, she looks to enlist the help of Yasuri Mutsune, head of the Kyotou-ryu school and hero of the rebellion. But when she arrives on the island where he lives in exile, she finds him dead, succeeded by his skilled yet slightly daft son Shichika. Undeterred, the two set off from the island in search of the swords armed only with Togami's sharp strategic mind and Shichika's powerful, swordless Kyotou-ryu.
In Japan, legends tell of a strong clan of warriors who fought unarmed and walked the path of the undefeated. Since the Heian period, this clan known as the Shura helped shape and form history as we know it with the help of their legendary Mutsu Enmei-Ryuu style. Watch history unfold in this epic tale as the Shura and their ancestors witness the days of the swordfighter Musashi, fight with the one-eyed Jubei Yagyu and help influence the fall of the Shogunate and Shinsengumi; and most importantly, touch the hearts and minds of everyone they meet…
Although both anime use quite a diffrend style there is some similarities (besides setting). The major one would be that both anime main characters fight unarmed, does'n't use a literal sword when fighting and in place of a sword, uses hands and legs as weapons. That particular keeps me interested when watching good fights and there is plenty of that in both anime.
Both anime focus on a lineage of individuals who use unarmed techniques against armed foes. Additionally the main characters (Shichika in the case of Katanagatari or the people of the Mutsu Enmei-ryuu) are seemingly aloof from the rest of the world, while their partners are far more knowledgeable/savvy about the world.
In a futuristic and wild west-inspired Japan, there are only two rules: the Number 1 rules the world and only the Number 2 can challenge him; these ranks are worn with pride in the manner of headbands. In these harsh times, Afro is a samurai who is on a mission for revenge – an evil gunman killed his father to become the Number 1, and it’s up to Afro to take him down in a shower of blood and entrails. He has mastered the art of the sword and become Number 2, but many others want to hold his title and the title of Number 1 for themselves. With competition and sword fights at every turn, can Afro finally exact his revenge?
The 'girl in the sky' is a legend passed down through the ranks of one special family. Armed with the magical puppet skills he learned from his mother, Yukito Kunisaki follows in her footsteps, traveling from place to place, ever searching for that girl in the sky, ever chasing after that legend. His journeys have led him to a small costal town where he meets a girl that has a peculiar interest in him - could she be the one? As events slowly start to unfold in front of his very eyes, Yukito finds himself amidst a story that spans a thousand summers...
While there are several differences between the two one thing that they both have in common is that right from the beginning they get the viewer interested in the characters and what happens to them. In addition both feature overall plots that span the time of a couple centuries but at the same time focusing on primarily on a pair on two people. Though Katanagatari does have some action in it and Air is just overall slow-paced if you liked one then you'll probably be interested in the other.
It is the era of Bakumatsu – the last years of the shogunate. In the general turmoil caused by warring groups with different political interests, a curious theatrical group known as the Yuyama Troupe is set out for revenge. They come across a mysterious young swordsman, Akizuki Youjirou, who seems to be burdened with a dark past. Thrown around by currents of history, powerful people from different factions and personal relations, Akizuki tries to fulfill his mission to destroy an ancient, cursed relic, the Lord’s Head, which has caused chaos and bloodshed for thousands of years.
Both series share the feeling of an epic journey, mixing adventure and action-packed fights with the search for supernatural artifacts and some more thought-provoking moment. They also have some historical references and a lot of different characters, some of whom, especially the main protagonists, do have a good amount of development. Oh, and they both have lots of dialogues (but most of them manage to be rather interesting).
Katanagatari is a bit more lighthearted and is generally easier to follow, but I'm fairly confident that fans of one won't be disappointed by the other.
Oboro, a naive, love-struck girl, is pledged to Gennosuke, an idealist. Both are successors to opposing ninja clans with a long history of hatred kept barely in check by a covenant of peace. Just as the two vow to reconcile the clans with their marriage, the shogun orders the feud to resume in order to resolve an internal struggle that threatens to tear the Tokugawa shogunate apart. Even worse, Oboro and Gennosuke themselves are forced to lead their clans in battle. Can the star-crossed lovers resist the brutal circumstances and remain true to their love as the death toll rises?