C: The Money of Soul and Possibility Control, Persona 4 the Animation Recommendations
Although these series are quite different in their mood and idea, they share the following two things:
(1) Protagonists in both series get in a mysterious parallel world and fight there using powerful "familiars" (actually, they're not usual familiars, but explaining them would be a spoiler, so let's leave it at that). The reasons for fighting and effect of the battle outcome are really different, but the process is pretty much the same: the familiars combat under their owners command invoking different technics and weapons, and that makes a really nice and impressive action.
(2) There is a mystery that protagonists are trying to figure out in
*Both animes have two different worlds. In Persona 4 there is the normal world and the TV world. In C there is the normal world and the Financial District.
*Both animes summon monsters using cards. In Persona 4 they are known as Personas, while in C they are known as Assets.
*The overall moral in both stories are extremely different
*The way each story progresses is different
Characters who use devils to fight other people in matches. Main character starts out weak but gradually grows stronger