Gandos: I'm going to offer a somewhat dissenting opinion here and say that it depends on what you look for in an RPG and how much you can tolerate some of the standard anime tropes.
More so than any other title in the Persona series (let alone the SMT series as a whole), Persona 4 comes off like a typical shounen anime series. This isn't to say that it doesn't have enough unique qualities to stand out from other such works or that it's bad. But if you don't like the idea of a game frequently deviating from the main plot in order to portray the cast doing typical teenager stuff (even if the main plot leaves something to be desired), you're not going to enjoy the game very much. ESPECIALLY the Vita version, who's primary addition is really even more of such inconsequential scenes.
Furthermore, if you're looking for challenging gameplay, you're not really going to find that here. To be fair, this applies to the Vita version more so than the PS2 version. While the original game wasn't exactly notably hard, it did still offer a decent challenge if you played on 'Hard'. The Vita version technically adds a harder difficulty, but the breath of options that exist to aid the player and some crucial changes to the boss encounters results in the overall challenge getting reduced significantly. Of course, an easier game might be exactly what you're looking for, so it's up to you how this squares with your own expectations.
Lastly, if you're expecting a lot of player freedom, you're setting yourself up for disappointment (though JRPGs in general usually don't offer that to begin with). In spite of its presentation, the game is still a dungeon crawler at its hearts, much like the other games in the SMT series; and it follows a fairly linear path (though it does have multiple endings). There is no 'overworld' to speak of; outside of dungeons, the game essentially consists of a series of glorified hubs that you travel between. And while the randomly generated dungeons do offer some bonus items for searching them thoroughly, there isn't really much exploration to be had.
That all said, if none of that puts you off, it's a pretty decent game with likeable enough characters to be worth playing at least once and it's one of the better titles the Vita has to offer. But I will give you one more warning. If you're at all interested in checking out the SMT series as a whole, I would HIGHLY recommend playing a different title before delving into Persona 4. This is because P4 deviates from the rest of the SMT series to a fair degree. If you use P4 as a jumping off point, you might be put off by how darker and more difficult the other SMT games are. If you're wondering what other games might be better to start with, you might find this (somewhat dated, but still mostly relevant) video by Rasen Bran to be informative:
https://www.youtube.com/watch?v=5XB00j8iPYg Anyway, I hope some of this information was useful to you. Happy gaming! =)