Rio Sakaki was raised by an unsympathetic father and a stepmother whose dream of a normal, happy life drove her to harass the poor girl and have her institutionalized. As a result, Rio developed suicidal tendencies and an aloof, distant personality that drove all potential friends away. But things change for the girl when she meets the studious, yet just as troubled Sahoko one day, and in time, Rio's icy exterior begins to melt. Together, the two girls quickly become fast friends and try to carve out their own happiness in a world that has neglected them.
One day, Natsuki was walking in the rain when she saw a high school girl with no umbrella. She gave the girl her umbrella on a whim and didn't see her again until her sister was married. For it seems that the girl, Michiko, is her new sister in law. Together the two begin a tumultuous friendship; Michiko is difficult to handle, yet Natsuki finds herself drawn to her...
On the way home from work, male-to-female transsexual Maho meets Fujiko, the estranged daughter of a well-to-do family. After realizing they live in the same apartment and both work night shifts, the pair soon becomes inseparable, due to their mutual jaded personalities and detachment from normal society. Between drinking tea and gardening, the two women discuss gender and the frames that society imposes on people.
In both these manga, two women from less-than-ideal backgrounds meet each other by chance one day and become close friends. Both have some very mild shoujo-ai elements (Pieta moreso).
Pieta has more romance and drama, whereas in Double House this is replaced by musing over the role of gender in society.
Tohru Honda might just be the unluckiest girl around. After a series of unfortunate events Tohru has no place to call home - that is, until the wealthy yet cursed Sohma family offer to take her in, in exchange for performing the household chores. However, soon Tohru discovers that there's much more to the Sohma family than meets the eye. Though shocked and surprised, Tohru promises to keep their secrets; but will the Sohma family approve of an outsider knowing who they really are?
It seems like every major character in Pieta and Fruits Basket is psychologically unstable. While they all have perfectly good reasons for being so (mostly stemming from their very unfortunate childhood circumstances), it still makes both manga rather angsty.
Pieta is targeted to a generally older audience, and lacks Fruits Basket's comedy, but both will appeal to those who like tragic character dramas.
After Juri's third suicide attempt, only her aunt Monica cares enough to help her. Monica is a nun who regularly visits convicts and, believing that Juri will provide some insight on these emotionally destitute men, invites her to come along. One such prisoner is Yuu, who is on death row for murder, but has refused all visitors because of the hypocrisy he sees in the religious and other self-proclaimed do-gooders. When the two meet, they realize they have lived through similar turmoil, and agree to reconvene weekly to try to make sense of their lives.
Two people that still bear the emotional scars from their tragic upbringings meet each other by accident, become fast friends, and try to make sense of their pasts.
Both are really sad, though Pieta isn't as well-written and tends towards angst.