Chiruran: Nibun no Ichi

Both have elements of the Shinsengumi, But Touken Ranbu is about historical swords transformed into men to protect history. The swords from the shinsengumi include Kashuu Kiyomitsu and Yamatonokami Yasusada two uchigatana wielded by Okita Souji, And Izuminokami Kanesada(uchigatana) and Horikawa Kunihiro(wakizashi) wielded by Hijikata Toshizou 

Both have elements of the Shinsengumi, But Touken Ranbu is about historical swords transformed into men to protect history. The swords from the shinsengumi include Izuminokami Kanesada(uchigatana) and Horikawa Kunihiro(wakizashi) wielded by Hijikata Toshizou 

Both are about the shinsengumi. But Hakuouki is more of a romance anime aimed at the female audience 

Hakouki O. might be a spin-off from a main series but the story pretty similar with Chiruran about daily life of shinsengumi in a chiby ver. Also both is only around 3 min in duration.