In the near future, some girls are born mutated. Known as Diclonius, this new species is believed to have been chosen by God to wipe out mankind. Unlike regular humans, Diclonius have two horns on their head and ‘vectors' - invisible ‘hands.' Contained within a research facility unknown to the world, the Diclonius are experimented upon mercilessly; many die or develop a hate for mankind. One such creature, Lucy, is said to be the first of the Diclonius. She escapes from the facility, but while fleeing she takes a bullet to the head and is seemingly killed. However, it seems Lucy isn't quite dead yet; she's instead developed an alternate personality called Nyuu. She's washed up on a shore where two people, Kouta and Yuka, find her and bring her home, unaware that such a monster still lurks within Nyuu.
In a post-apocalyptic world, humans, robots and cyborgs live in the Scrapyard - a landscape of twisted, rusted junk made up of the garbage sent from the above city of Zalem. In this place, the inventor Ido finds a partially-destroyed cyborg amidst the rubble, gives her a new body and names her Gally. With no memory of her past and an instinctual ability to use a powerful martial art known as the Panzer Kunst, Gally matures and relearns life's lessons while she travels the broken landscape, struggles to remember who she is and where she came from, and discovers the mysteries of Zalem.
Both series star a non-human woman with superhuman powers (although the star of Elfen Lied is more of a villain, while the star of Battle Angel Alita is clearly a hero). Both stories are very dark & violent, and raise questions about what exactly defines "human".