Persona vs Senki Zesshou Symphogear
Connection:
Both are young women who've experienced severe traumatic events, resulting in someone sacrificing their lives for them (Sumire's sister Kasumi and Kanade Amou respectively), causing them to be scarred both mentally and physically by this. Eventually they move on from it and face life with their heads held high and a smile on their face, though they still feel guilt over this incident
Both joined a group dedicated to fighting dark beings who threaten the world, possessing powers similar to their own (The Phantom Thieves and S.O.N.G respectively), with said dark beings being a usual threat to the main team (Shadows and Noise)
Both even had a crush on one of the members, which they have trouble telling them (Joker/Ren Amamiya and Miku Kohinata respectively)
Both sometimes went into berserker forms due to emotional stress (Sumire refusing to accept the truth about her being brainwashed and Hibiki going into her berserk form a few times)
Both their own powers are incomplete compared to the others, and after said powers made them go berserk, they lost them; but soon enough regained them at their proper full power (Sumire not using her powers for a while until the Maruki incident where she lost control of them for a bit, but regained them due to coming to terms with her survivor's guilt, and Hibiki having trouble controlling Gungnir's power until she was able to control them due to her drive and passion to save others)
Both their final fight were against a god-like entity that wanted to remake the world to how they see fit, until they turn to being reformed, but in different ways (Sumire and the Phantom Thieves showing Maruki there's more to humanity than changing cognition/reality and changing his views, and Hibiki getting Miku out of Shem-Ha's body so she can stop her from "returning the world to the way it was 5000 years ago")
Both are related to music as connections between Kasumi and Sumire is a dance (Sumire is seen dancing while holding an umbrella on a rainy road on the animated opening of Royal, referencing to her sister Kasumi's death), and the main connection between Kanade and Hibiki is a song (Kanade being written with the kanji for "to play (music)", and Hibiki means "a sound", "a ring", or "an echo" and used as a verb, it can mean to "resound/resonate")