Fallout 2 improves upon the foundation of Fallout 1 in many ways and when people are reminiscing about "the good old Fallouts", the things they're thinking about are almost entirely from Fallout 2.
The combat is a smoother experience and while it has some issues (that I'll get into later), it is a generally better game to play. The writing is, on average, better than FO1 (with the caveat that the humor tends to be much more abrasive - either opening mocking the game or its characters, or winking and nodding at how silly videogames are. I'm not a fan of either of those things but your mileage may vary). The crowning bit of this game, though is the ending. It's a pretty great ending that actually sets up one of the biggest facts of the setting that the Bethesda games later leaned into quite heavily.
But before I get too much further or get into too much detail, I need to get into some of the bad stuff. First off, the game is deeply racist. There's the very obvious stuff like Hakunin and Sulik both being bizarre mish-mashes of actual cultural traditions which result in deeply offensive caricatures. But there's also an idea that is pervasive in post-apocalyptic fiction that humanity would somehow "regress" back to more "basic" types of cultural, specifically that tribal or indigenous cultures are somehow "lesser" than more "advanced" cultures. This idea is straight-up racist and deeply offensive to indigenous peoples because it assumes that they are somehow inherently less intelligent and less capable because they live in tents and not in bombed-out buildings. Fallout 2 then takes it a step further and leans into this idea by having people (especially in the early game) refer to your character as "a tribal" and will talk down to you because of it. The game never seems to do this knowingly, either, because it never really remarks on how that's bad or anything - it just considers it a truth of the setting. On top of that, there's the classic Fallout racism that is in each and every game with ghouls. If you have the ghoul companion then you're going to have to tell him to wait outside whenever you enter a building because people 'don't like his kind around here.' The game at least seems aware of what it's doing with this but still isn't doing much to make note that people are being racist and that's a bad thing. It's once again just considered a factual part of the fiction. At least when Fallout 1 was racist it had the good graces to be ashamed and try to hide it a bit.
My other main issue with the game is that the combat, while an improvement FO1, is a slog. At the start it's okay because it's just the beginning and, hey, whatever, it's fine. But by the end of the game, nothing about the combat has changed in any meaningful way except now instead of fighting geckos and rad scorpions, you're fighting groups of Enclave soldiers in power armor. So you either have to do even more of this not-great combat to level up to even up the playing field so you can maybe survive all these random encounters or dump a bunch of your points into the Outdoorsman skill so you can avoid the random encounters completely. It's a poorly thought out system that seems to punish you for avoiding combat (because you get less experience) but also punish you for engaging in combat (by draining resources like health and ammo). It's not fun at all and is only worse because the game never adds any sort of interesting combat mechanics for you to implement. There are no skills, no special weapons, nothing that would make you approach combat in a different or more interesting way. The entire game you're either shooting things with a gun or hitting them in melee.
The issues with the combat connect into the later parts of the game where for the final third or so, the game sends you on a series of very long fetch quests. "Oh you just got here, we need you to go somewhere else to get one item or talk to a person." Over and over and over again. So you end up having tons of these high-level encounters while you're running all across the map to try and find every macguffin to move the plot along. It's an awful grind that exists only to drag out the length of the game. The actual end area of the Enclave Base is good but I'm not sure if it's even fully worth how much of an awful slog all these fetch quests are.
And that brings us to the ending which, outside of one specific part, I think it's pretty good! The most interesting parts of the story are here with some big reveals about the Enclave and the truth about the world as a whole. It should be said though, that none of those interesting reveals are ever hinted at when they really should have been just to let you know that something bigger was going on and not just evil people being cartoon villains (okay, it still is somewhat that but not entirely).
That one issue I mentioned about the ending is, once again, combat. After everything is said and done, you have to fight through a final boss. Despite Fallout 2 being touted as the game you can talk your way through, you still have to fight the biggest damage sponge in the game (and on a time limit, no less!) For a game that encourages so many different types of play and wants you to play around with how you interact with the world, it's absolutely bizarre that the ending is a fight with a big slab of beef with a minigun.
So overall the game is an improvement over Fallout 1 and I'd say a pretty alright game. Just don't be afraid to open up a character editor and give yourself some stats so you don't have to deal with atrocious end-game combat. It's a game you play for the story, there's no good reason to suffer through unrelated parts just to get to the good bits.
Oh and one final thought: I just want to give a shoutout to the talking scorpion. It's the funniest gag in the entire game and maybe the whole franchise. It plays within the game's setting (instead of most of the humor which can get pretty meta both about Fallout and about videogames as a whole) but it also has interactions with the game's mechanics and the player's stats. It's very clever and silly and fun and good.