Honkai Impact 3rd vs Senki Zesshou Symphogear
Connection:
Both are humans who have lived throughout the eras for numerous centuries, being noted for their driven, strict, stoic, and studious behavior, and were raised by lone fathers who trained them to masterfully dabble in a community practice (martial arts and alchemy respectively). However, a late tragedy would turn their life upside-down and separate them from their fathers (Fu Hua lost her entire home city to a Honkai Impact, while Carol witnessed her father being burned at the stake), leading to them losing most of their kind-hearted manners and developing a new cold and hardened resolve (Fu Hua devoted to use her fighting skills to end the threat of the Honkai, whereas Carol misinterpreted her father's desire to learn more about the world, and sought to use her alchemy to "dissect" it in order to end miracles)
Both have been former members of a group that acted on opposite reasons which have since been wiped out (Fire Moth, which sought to eliminate Honkai threats, and the Alchemic Cult, which Carol formed in her drive to destroy the world) and were part of projects that involved working with the human physiology (Fu Hua became a MANTIS-enhanced human soldier infused with Honkai DNA, whereas Carol created countless Homunculus bodies to reincarnate into), which gave them a form of immortality that let them live on for achieving their goal.
Both were also the previous masters of a small group of disciples who wielded a small portion of their skills and abilities (Fu Hua's many students of her Taixuan school and Carol's Autoscorers respectively)
Both also attained powerful relics that bolstered their combat prowess (The Key of Sentience and Daur da Bláo, respectively), which allows them to channel a specific energy (Honkai energy and Phonic Gain respectively) into immensely powerful attacks, one of which, despite its unmatched power, comes at a grave cost of burning away their memories (The Edge of Taixuan and alchemic memory combustion, respectively)
Both also once took a risk at sacrificing themselves, though the kind-hearted protagonist of their series inspired them to push on and re-evaluate their selfish perspectives (Kiana Kaslana and Hibiki Tachibana respectively)
Both have most notably formed a connection to a being who largely shares their appearance, yet has a personality the polar opposite of theirs (Herrscher of Sentience and Elfnein respectively), who they'd later merge with to share body and consciousness together to some degree before separating, though from different circumstances (Herrscher of Sentience grew annoyed with Fu Hua attempting to use her suppressed power and separated into her own physical form, while Carol's overconsumption of her own memories in the fight against Shem-Ha caused her consciousness to die and leave Elfnein in control of her body)
