After hearing how popular the duology was for old-school SMT fans, this was on the top of my hitlist after completing Persona 5. Going in, I was hearing everyone describe this as a dark and mature game and I was left a bit disappointed, unfortunately. This game has its moments here and there, but I was expecting something way darker than what we got.
That's not to say the game is bad by any means. It's a huge step up from Innocent Sin in terms of characterization and story. I liked the cast a lot more in this one because they felt real and fleshed out. I'm a particular fan of Baofu he's a fun character who gets some great moments with the rest of the party. Also happy we got to see Katsuya as a playable character and his antics with Tatsuya in particular are adorable. Overall, the game's cast is the strongest aspect of the story for me and I think that is due in part to them being actual adults. There's a very cute touch where Tatsuya is unable to purchase alcoholic drinks because he's underage which I thought was delightful.
I think the plot doesn't go nearly as crazy as Innocent Sin does, though, which was my favorite part of that game. Innocent Sin really leaned into the idea of rumor becoming reality using commonly held conspiracy theories and turning them into pivotal story points which I thought was more interesting than Eternal Punishment.
The gameplay's more the same. A bit archaic but I eventually found myself enjoying it. There's a catharsis to blasting an any group with Giga Cyclone and raking in some experience. In particular, I wish they'd bring back Fusion Spells in future Persona games because they make party building more important and interesting. I also love the mutation mechanic that further incentivizes using fusion spells and can often result in some unexpected developments.
While I still prefer Persona 5 Royal I did greatly enjoy myself with Eternal Punishment and I hope Atlus eventually remakes the duology one day because these games deserve to get some modernization for modern players to experience.

IT TOOK FOREVER BUT I BEAT IT

AND IT WAS SO WORTH IT.

The journey to me beating this game was over a year long. I definitely enjoyed the gameplay and story more than Innocent Sin, especially Tatsuya just being so interesting here.

This is easily the best Persona game. It's story is a follow up to Innocent Sin, and while it arguably doesn't hit the highs of storyline that game did, it just feels very good in a way. It has a cast of entirely adults, something I really wish Persona would try again today, but most importantly is that they're ALL likable characters. In Persona 3, 4, and 5, there's always at least one character that makes me think "I hate you, please stop talking" every time they open their mouth. Both games in the Persona 2 duology have none of those.

The gameplay is the thing people cite as an issue in this game, and I couldn't disagree more. It's gameplay is the peak of the franchise, with some small issues I admit are pain points. I think a lot of people misunderstand the combat as being standard fare of turn-based RPGs where you click a single move every turn. In reality, this game is based on actions repeating, until you interrupt the action to change commands on your characters. For example, on the Joker boss battles, when Old Maid is cast, it's best to put your entire party on Defend. Then interrupt the action after each character and see if they were changed to "Attack", and that's how you determine who got hit with the Joker.

Speaking of this game's bosses, they're incredibly strong and really stimulate your brain. Some of them may feel out of your reach the first attempt or two, but 99.9999% of the time, you absolutely have the tools to be able to do it without having to grind at all. For instance, there's a late game boss that restores about 800 HP per turn. You might think this sounds obnoxious, but you can use Fusion attacks to stack up enough damage to out-damage the heal.

There are some pain points in the game for sure. The biggest one to me is the summon system to obtain new Personas. Like Innocent Sin, you have to negotiate cards out of demons to be able to summon Personas. Making a pact with a demon gives you "Free" cards that you can have converted to any Arcana card you want (except Fool). This system can become quite the grind, however Eternal Punishment has a significant way of cutting this down. Innocent Sin's biggest issue with negotiation was the sheer number of options you had. Every character had four actions they could perform individually, and then you also have a unique action for each combination of characters. If you weren't sure what to do based on a demon's personality, this made things VERY hard to trial and error. Eternal Punishment fixes this by streamlining negotiation. Every character individually only has one action, and combinations of course have their unique interaction. Some of these combinations may end up just deferring it to one character and being the same result, and some may change over the course of the game. The trick was often to make a pact or two in the dungeon you're on, and then every time you see that demon, negotiate cards out of it so you get the "Free" cards too. The "Free" cards become your lifeline for getting new Personas.

The ending of the game is beautiful, the result of you playing two entire games to get to this point and the payoff is quite satisfying.

This version of the game is solid and very playable today, however I understand why you might have some issues with the UI and speed of the game. Some of these issues are solved by the PSP version of the game, which has a fan translation patch available on the Internet.

Persona 2 Eternal Punishment is by far the most derivative mainline Persona game. It's simultaneously a sequel to Innocent Sin AND Persona 1, and reuses a lot of elements from the former. Despite that, It manages to surpass it's predecessor, and refines and improves a lot of the problems that game had.
Pros: The gameplay in this game, while still not amazing, is significantly better than Innocent Sin's. It expects you to have played Innocent Sin and expects you to take advantage of all the vast myriad of obscure gameplay mechanics and shops available for use. The game stops pulling its punches and gets significantly harder, and the difficulty is much needed. The strategies I was using in Innocent Sin stopped working, and I had to adapt to new strategies, and build team compositions around being able to form proper Fusion Spells. The game still has the tedium and the slowness of Innocent Sin, but it's more entertaining because it expects a lot more of you. Some people call this the hardest Persona game, but I don't know if I would agree. I didn't struggle with it that much more than I did Innocent Sin. I basically steamrolled the entire final dungeon. The difference is, I would say, is that with Innocent Sin I was barely trying and struggled, and with Eternal Punishment I was aware of it's reputation and was trying as hard as possible and still struggled. Either way, if you can go through the game taking the most possible advantage of Fusion Spells and Mutations and Skill Cards, you shouldn't have the hardest time. The story in the game is also great. I love how different it is from every other game in the series, aided by the fact that it has a fully adult cast. I still think I like Innocent Sin's story just a bit more, but Eternal Punishment still has everything great that game had. The characters are still super entertaining, and I especially love how Tatsuya was characterized in this game. Turning a silent protagonist into an actual character isn't something that can be done easily, but it was pulled off flawlessly here and feels so natural. The game's contact system is much improved. It's streamlined from Innocent Sin to be less complicated and I think it works very well to remove some of the tedium of demon contact. The rumor system also returns and is also improved. Rumors are much more varied and control much more. There's a lot to love here.
Cons: The battle system, while better, still has a lot of the flaws of Innocent Sin. In addition, this game takes a bit too much from Innocent Sin. It's justified incredibly well within the story, but a lot of things are reused. Some dungeons in the game are completely original and those tend to be the best and most interesting. Other dungeons take place in the same place as dungeons from Innocent Sin, and as a result use the same visuals and environments, but still contain different layouts, and those are much less interesting. Other dungeons are literally ripped straight from Innocent Sin, with the exact same layout and everything. Those are the ones I really take issue with. It feels like a slog and a waste of time to have to do everything all over again. Again, it's justified well within the story, and it's not too big of an issue, but it was an annoyance I had. Another thing I don't like about this game is it's characterization of Maya. Maya was turned into this game's silent protagonist and while I like that doing so allowed Tatsuya to become his own character, I don't like how much Maya's character had to be reduced. Maya was the emotional core of the group in Innocent Sin, and her trauma and backstory was a major focus of that game. It just feels awkward that none of that is really focused on much anymore, because all Maya says in this game is "...." and "Maya smiled gently" or something.
Overall: This is another must play game, even more so than Innocent Sin, despite being it's direct sequel. It has a lot of the same strengths as Innocent Sin and improves upon its biggest flaws.