If you're looking for manga similar to Persona 3 the Movie 3: Falling Down, you might like these titles.
I, Sakuya Hoshi, am just a normal high school student who attends Suijou Academy. But for some reason, every night I was being 'called' by a 'creepy' dream. In the dream is a town of never ending night. No sign of people there besides me; instead of people there are 'monsters'. That's the kind of dangerous world it is. With the girl I met in my dream, Akeno Gasukamori, we try to find a way to somehow escape this endless nightmare. Will we ever safely get out of this endless nightmare, with monsters after us and other repeating horrors? And exactly what or who awaits us in the end...?!
War between the kingdom of Ragnanival, led by the king Odin, and the realm of Ringford, led by the queen Elfaria has devastated the country of Valentine, of which only scattered ruins remain. The story is told from the perspective of five characters whose stories intertwine: Gwendolyn, valkyrie and younger daughter of Odin; Cornelius, prince of the neutral country of Titania; Mercedes, daughter of Elfaria and princess of Ringford; Oswald, a shadow knight and agent of Ringford; and Velvet, a survivor of Valentine's devastation.
Ragna the Bloodedge. That man is nicknamed Grim Reaper and possesses the power of Azure Grimoire. Yet, he awakens in an unfamiliar land and has lost both the Azure’s power and his memory. In this unknown world, he comes across Celica, a girl who is able to use healing magic, and a beastkin warrior named Mitsuyoshi. Their journey is closely related to the Black Beast, a being which drive humanity to devastation. However…
Demitri barges into Morrigan's bedroom and demands she fight him. Suddenly, Jedah appears with a new friend!
Focuses on Yosuke Hanamura's life before the events of Persona 4, while occasionally re-telling events from the game.