It's about how troublesome could be to try to live as a normal citizen if you were born or made yourself an outcast of it. It's about thing to have a personal growt. It's about one young woman trying to help/implement that growth into others and the helplessness she feels if/when she doesn't win that battle.
Both are dramas with female leads which are cute, fragile ladies with glasses on a noble government position which are trying to straighten up a social outcast by trying to solve some of their problems. The main difference is that in Gokusen the heroine uses martial arts to scare of the people, which are trying to hurt the people she is trying to protect... In Zenkamono the heroine is left alone with the system.