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.
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.
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".
Once again, I rec these two manga based on the world around them. Both are futuristic post-apocalyptic settings with horrifying imagery. If you like that sort of backdrop give these two manga a try.
In 2033, a boy named Neji awakens with little memory of himself or his past. According to Luzer, his caretaker, Neji was executed ten years ago for serious crimes and now a guinea pig for Gera, a national ESP research center. He exists as a Revenant, an assassin with psychic powers, and has no identity in the outside world. Faced with tragedy and death, Neji must find his place in this new world.
BAA is way, WAY better than Neji, but they are decent recs for each other. Both are sci fi titles that have a few distinct arcs and have a similar feel, though Neji is far more confusing and less awesome in general.
The Legend of Mother Sarah and Battle Angel Alita take place in a land filled with human trash and a 'kill or be killed' struggle to survive, where our kickass female leads, Sarah and Alita, treck on a journey to discover and uncover the past. Be it uncovering the whereabouts of her children or Alita discovering her past self, Sarah and Alita are strong, intelligent women in a brutal and corrupted world. Similar atmosphere, badass women leads, incredible art, and phenominal plot are but the basics that connect these two of a kind manga.