The game is fine, good sometimes even, but it has pretty big problems. There will be minor spoilers here, but nothing revealing the game's main antagonist(s).
As far as what I don't have issues with:
-The music is spot on, as it usually is in Persona games.
-The combat system is generally good, but in my opinion worse than Persona 3's as there is only one type of physical attack. Makes physical attacks and selecting them in each Persona less interesting.
-The overall presentation is good for being a PS2 game, though there are some scenes where it feels like they just fully brightened all the textures and didn't do much to limit their hardware's deficiency.
-The gameplay loop outside the main story of doing social links is good, albeit time consuming. Don't play this game if you can't sink a lot of hours into it.
With that out of the way, I'd like to discuss all the characters you meet, outside the protagonist as like Persona 3, they are fulfilling a sorta self-insert role again.
-Yosuke: For the first half of the game, or about before Rise shows up, he's actually one of the best if not the best-written party member. After that though, it feels like he gets a lot more flanderized and he gets obsessed over topics like being manly, or being needlessly homophobic to a point that is just kinda annoying. A lot of the latter would be less of an issue if the whole him being in the closet thing wasn't cut from the game, but its not there, so I'm going to treat his character as such.
-Chie: She's kinda funny, but there's basically nothing to this character over liking fighting, wanting to protect people, and eating meat. She's just funny and there's not much to write home about.
-Teddie: Hot take, but I like Teddie. To start, I think he's really, really funny; yes, he does things a good person shouldn't do, but he's also not like the rest of the cast. He's often responsible for some of the more entertaining stuff happening on screen, and there's a surprising amount of depth to the character as the game goes on. He does get pretty grating while he acts as the sort of dungeon analysis person, though. Luckily that doesn't last for the whole game.
-Yukiko: She's also funny, without too much to write home about. There could've been something about her leaving her inn, but as many of the social links in Persona 4, she undermines all that stuff later. I do like the scenes where she starts laughing uncontrollably at first, but something is missing in those as the game goes along. All in all she's not bad, but just not super interesting.
-Kanji: I think there's a little more to Kanji than the others here; he's got the right level of empty-headedness that makes me amusing while not getting annoying. His whole conflict on trying to be a confident guy while also embracing the side of him that likes cute stuff that isn't traditionally masculine also makes for okay social commentary. I say ok because that's mixed in with one of the themes of his dungeon being, "I'm not actually gay, I just thought I was gay." A bit unnecessary there and unfortunately takes away from the stronger parts of him, but still, my opinion's overall positive.
-Rise: I don't like Rise; I don't think she's outwardly terrible, but I also just don't like her; she's at best, very, very ok. As for why that is, she just feels like a character that exists to be the protagonist's obvious romantic partner; not in the same way as say a Yukari that is a safe partner, but someone who does not exist or function on their own as a character. It doesn't help that her social link suffers as the same problem as Yukiko's as its all about undermining any decisions she made as a person before. Otherwise she just gets too flirty too fast with the protagonist in a way that doesn't feel real and comes off as annoying. Basically, I don't feel like there was a real character here; it felt like she was an object at many points.
-Naoto: Similar case to Kanji, except the bad stuff is kinda worse here, as the climax of the character's dungeon involves rejecting a sex operation while the game spouts some pretty terfy stuff at you about how nothing can change your sex and all that. On the other hand though, a character about how women can do things men traditionally too would be too is a good idea, the execution here just kinda misses, especially as the character even feels borderline dysphoric in some of their behavior, like in the hot springs scene. Basically, Naoto partially felt like the writers wrote their idea of a trans person, which is according to them, someone that's in denial of their "true" gender. Its especially hard to give the benefit of the doubt here as the director has really only gotten worse when its comes to depictions of marginalized groups.
As for characters not in the main party, two deserve shout-outs for me:
-Adachi: He's funny. Whenever he's on screen, I have a big smile on my face.
-Ai Ebihara: I think she might have the best social link in the game, and definitely makes for one of the more interesting romantic partners with the protagonist in my opinion. She's not perfect, she has flaws, and even starts the social link out as an asshole, but I think all of that is what makes her social link much more interesting than honestly all the female party members. It just feels like there's actually something going on with this character beyond surface-level analysis.
So, how's the story in this game? Well... its once again, okay. I for one preferred my time doing social links and min-maxing the life simulator over the story in this game, which by no means was bad, with the mystery revolving around the murders in Inaba being decent up to a point, but after the end of December, all the story elements of the game feel tacked on and unnecessary, including the true ending. It also feels like a repeat of Persona 3 in a lot of ways that is less earned and doesn't have any serious ramifications involved unlike that game. It feels like there just isn't any stakes, if I was to describe it one way. Doesn't help that the game has issues with tonal consistency; I can't quite wrap my finger on it, but its different than say Danganronpa where the game is intricately balancing humor and tragedy. It might be the game's lack of stakes messing up the balance here.
In conclusion, if you liked Persona 3's life simulator and JRPG stuff, you'll like this game. If you liked Persona 3 for its writing and were just stomaching the other stuff, this one's not for you. The game's writing leaves a lot to be desired despite some hints of the genius from the previous game and some good characters here and there. Its certainly not a bad game, but it only manages to be a fine one.
As far as what I don't have issues with:
-The music is spot on, as it usually is in Persona games.
-The combat system is generally good, but in my opinion worse than Persona 3's as there is only one type of physical attack. Makes physical attacks and selecting them in each Persona less interesting.
-The overall presentation is good for being a PS2 game, though there are some scenes where it feels like they just fully brightened all the textures and didn't do much to limit their hardware's deficiency.
-The gameplay loop outside the main story of doing social links is good, albeit time consuming. Don't play this game if you can't sink a lot of hours into it.
With that out of the way, I'd like to discuss all the characters you meet, outside the protagonist as like Persona 3, they are fulfilling a sorta self-insert role again.
-Yosuke: For the first half of the game, or about before Rise shows up, he's actually one of the best if not the best-written party member. After that though, it feels like he gets a lot more flanderized and he gets obsessed over topics like being manly, or being needlessly homophobic to a point that is just kinda annoying. A lot of the latter would be less of an issue if the whole him being in the closet thing wasn't cut from the game, but its not there, so I'm going to treat his character as such.
-Chie: She's kinda funny, but there's basically nothing to this character over liking fighting, wanting to protect people, and eating meat. She's just funny and there's not much to write home about.
-Teddie: Hot take, but I like Teddie. To start, I think he's really, really funny; yes, he does things a good person shouldn't do, but he's also not like the rest of the cast. He's often responsible for some of the more entertaining stuff happening on screen, and there's a surprising amount of depth to the character as the game goes on. He does get pretty grating while he acts as the sort of dungeon analysis person, though. Luckily that doesn't last for the whole game.
-Yukiko: She's also funny, without too much to write home about. There could've been something about her leaving her inn, but as many of the social links in Persona 4, she undermines all that stuff later. I do like the scenes where she starts laughing uncontrollably at first, but something is missing in those as the game goes along. All in all she's not bad, but just not super interesting.
-Kanji: I think there's a little more to Kanji than the others here; he's got the right level of empty-headedness that makes me amusing while not getting annoying. His whole conflict on trying to be a confident guy while also embracing the side of him that likes cute stuff that isn't traditionally masculine also makes for okay social commentary. I say ok because that's mixed in with one of the themes of his dungeon being, "I'm not actually gay, I just thought I was gay." A bit unnecessary there and unfortunately takes away from the stronger parts of him, but still, my opinion's overall positive.
-Rise: I don't like Rise; I don't think she's outwardly terrible, but I also just don't like her; she's at best, very, very ok. As for why that is, she just feels like a character that exists to be the protagonist's obvious romantic partner; not in the same way as say a Yukari that is a safe partner, but someone who does not exist or function on their own as a character. It doesn't help that her social link suffers as the same problem as Yukiko's as its all about undermining any decisions she made as a person before. Otherwise she just gets too flirty too fast with the protagonist in a way that doesn't feel real and comes off as annoying. Basically, I don't feel like there was a real character here; it felt like she was an object at many points.
-Naoto: Similar case to Kanji, except the bad stuff is kinda worse here, as the climax of the character's dungeon involves rejecting a sex operation while the game spouts some pretty terfy stuff at you about how nothing can change your sex and all that. On the other hand though, a character about how women can do things men traditionally too would be too is a good idea, the execution here just kinda misses, especially as the character even feels borderline dysphoric in some of their behavior, like in the hot springs scene. Basically, Naoto partially felt like the writers wrote their idea of a trans person, which is according to them, someone that's in denial of their "true" gender. Its especially hard to give the benefit of the doubt here as the director has really only gotten worse when its comes to depictions of marginalized groups.
As for characters not in the main party, two deserve shout-outs for me:
-Adachi: He's funny. Whenever he's on screen, I have a big smile on my face.
-Ai Ebihara: I think she might have the best social link in the game, and definitely makes for one of the more interesting romantic partners with the protagonist in my opinion. She's not perfect, she has flaws, and even starts the social link out as an asshole, but I think all of that is what makes her social link much more interesting than honestly all the female party members. It just feels like there's actually something going on with this character beyond surface-level analysis.
So, how's the story in this game? Well... its once again, okay. I for one preferred my time doing social links and min-maxing the life simulator over the story in this game, which by no means was bad, with the mystery revolving around the murders in Inaba being decent up to a point, but after the end of December, all the story elements of the game feel tacked on and unnecessary, including the true ending. It also feels like a repeat of Persona 3 in a lot of ways that is less earned and doesn't have any serious ramifications involved unlike that game. It feels like there just isn't any stakes, if I was to describe it one way. Doesn't help that the game has issues with tonal consistency; I can't quite wrap my finger on it, but its different than say Danganronpa where the game is intricately balancing humor and tragedy. It might be the game's lack of stakes messing up the balance here.
In conclusion, if you liked Persona 3's life simulator and JRPG stuff, you'll like this game. If you liked Persona 3 for its writing and were just stomaching the other stuff, this one's not for you. The game's writing leaves a lot to be desired despite some hints of the genius from the previous game and some good characters here and there. Its certainly not a bad game, but it only manages to be a fine one.