Or to put it another way, what does the Persona series have that others don't. Something that would make you choose them over other RPGs, like Final Fantasty.
For me, it would have to be the sense of realism that's missing in most RPGs. Anyone can write a story, but it takes a lot more to make it, and the characters, feel real, feel possible.
I shouldn't have to mention this, but don't turn this thread into some kinda argument, instead focus on the question itself, and the longer your explanation, the better we can understand.