Regardless of how you feel about JRPGs, the one thing you can say about the Persona series is that it has consistently gotten better and worked on its problem areas with every new release. Leaving the "hardcore grinding/dungeon crawling/forum dick-waving" behind for the mainline Shin Megami Tensei series to cover, Persona has branched out into a more playable and accessible story- and character-driven game, while still giving a fair amount of challenge and requiring a fair amount of thinking and strategy in battle. Persona 3 was great, but this entry has tweaked the formula even closer to perfection and is an even better experience on the whole.
Persona 4 runs on a tweaked version of Persona 3's engine, so the experience isn't all that different, but all those little tweaks do add up to some big changes for the better. As with Persona 3, you play as a teenager transferring to a new high school for a year. Your parents are going overseas to do a contract job or something for the year, so you're packed off to live with an uncle and cousin you've never met before, and spend the year living in the rural town of Inaba. Of course, not long after you arrive you start having dreams of good ol' Igor and the Velvet Room, who awakens you to your Persona-summoning power and tells you you'll have the rest of the school year to solve a mystery. So you'll juggle your investigations of the supernatural world found by entering TVs with the normal daily grind of a high school student - exams, dating, Brocializing and working for pocket cash.
The biggest difference from Persona 3 is that in combat, you now can give direct orders to your party members rather than being forced to rely on a sometimes-flaky AI (though flaky AI is still an option too if you like that for whatever reason.) Also, instead of having one mega-dungeon, there are a number of smaller dungeons. The flow of the game is also a little different. As with Persona 3, roughly once a month there's a major event that requires you to fight a boss. However, you're no longer on a fixed schedule of a boss fight every full moon, with the rest of the dungeon open to exploration at your leisure. You have roughly a month from the appearance of each dungeon to complete it, or a major character who is trapped in there dies and the game ends (or more accurately, gives you the option of returning to an auto-save from a week earlier to try again.) To first even find the dungeon, however, you usually have to do a little detective work around town, to get clues about the person who disappeared into it. Once you know enough about them, your psychic-medium character can locate them in the fog world and lead you to their dungeon. You have to get to the top and beat their boss before the fog returns to Inaba, however, which always happens after 2 or more straight days of rain. Since you can only see a weather forecast for a week in advance, on the first playthrough there's more of a sense of tension since you're never totally sure how much time you have left until those two rainy days followed by clouds appear on the schedule.
What really makes Persona 4 seem like an improved experience, however, is simply the writing and the characters. Both were pretty good in the previous game, but are excellent here, and with a much niftier and more engaging central premise. Coupled with very good voice acting and a generally excellent localization, this is one of the better story-driven games I've ever played.
Though generally top-tier, there are still some obstacles to enjoyment here. Mostly they apply to those who don't already enjoy JRPGs and anime overtones. This is a very wordy game with a lot of passive reading and watching; you get a "trial by fire" in the first two hours of gameplay, which is nothing but going from one cutscene to another with rare opportunities to save. There's also the aesthetic. The game is significantly deeper than the usual "anime high school teen comedy/drama" sort of thing, but those allergic to J-Pop may have a reaction to the soundtrack. I'm no fan of the genre, but I liked the soundtrack (or at least tolerated it) for the same reason as Persona 3; catchy melodies paired up with muffled and Engrishy lyrics that are easy to mishear hilariously, with lines like "Hard dick, dick keeps on pounding!"
and "California potato power!"
Even if all that's not a problem to you, there's still a few disappointing items. The main one for me is how much of the enemy roster was completely re-used from Persona 3. I know RPGs almost always recycle enemies, but between installments they usually at least give them a re-draw or re-render. This one looks like they just lifted out all the character models from the previous game and used them over again, with only a sprinkling of new enemies introduced (aside from the bosses, some of which are really impressive-looking.) I was also frustrated by how the game artificially sucks time from you in nonsensical ways. For example, during exam week you lose your afternoons and evenings entirely, and often an "event" with a character that only involves talking to them for a minute somehow eats up that entire block of time. With five "personal characteristics" to grind up instead of three now, and all the social links and side-quests, one year ends up not seeming like nearly enough time, but a lot of that is due to artificial time theft by the game. I thought this was actually the one area where Persona 3 was much better thought out. Finally, the game has multiple endings, and getting the "true" ending (which opens up the real final dungeon and last boss) is one of the most obtuse sequences I've ever seen in a game. If you didn't know it was coming by hearing from someone else or reading a guide beforehand, and have at least SOME idea of what to do, I don't see how you'd ever find it on your own. Atlus got just a bit too cute for their own good with this particular element.
Minor problems aside, if you enjoy JRPGs at all snap this one up while they're still pressing it and you can get new copies with the soundtrack disc for 20 bucks.