I agree with a lot that said about dipping into the PSP back catalog for that style of RPG. Sadly, I don't think there are a lot of options for Vita-specific RPGs (most of the recent games of that ilk that I can think of are over on the 3DS: SMT4 and Soul Hackers 3DS were both stellar).
If you particularly enjoy the way P4 story works, you might look into Visual Novel genre, which surprising has some decent representation on Vita. Recommend Vita games of that ilk: the Dangan Ronpa series and Virtue's Last Reward. They are really good complements to P4 because they all revolve around young people solving dark mysteries in extreme situations. Patrick has done a decent amount of converge on them.