They both have same director. They both deal with love and duty vs honour, and a lower caste samurai being asked to kill someone he is reluctant to.

same director - same themes of love and difficult decisions about honour

Both have the same director and are about low ranking samurai who deal with love, impending poverty, and honour.

both films are directed by Kurosawa Kiyoshi and star actor Show Aikawa. They also both share the theme of a father who kidnaps a man whom he thinks to be his daughter's killer.

Both movies share the theme of a young guy sent to prison who is given a hard time by other inmates

Both movies are based on the life of Yoshi Shiratori, an anti-hero in Japanese culture, who is famous for having escaped from prison four times. Both movies show a special relationship between a prison warden and one of his inmates, who is constantly trying to escape while being abused by the prison staff.

both are about corruption, child exploitation, and pedophilia

Both movies share VERY similar plot lines. Both involve two boyhood friends. One grows up to become a cop, the other seems to have had an unknown fate. The cop investigates a series of serial killings throughout the movie and makes a startling discovery about the fate of his boyhood friend.

Both star Tsumabuki Satoshi
Both are crime/mystery genres

Both movies involve the abuse of vulnerable deaf children

Both 'Mountain Cry' and 'Blind Mountain' are about small-minded villagers in a remote chinese village.