Not just one of the best sequels ever made, Fallout 2 is also a legitimate contender for best game of all time.
I've written a pretty extensive review for the original and as I go to write this, I find that most of what I said applies here...and then some.
Fallout 2 does little less than define what a perfect sequel should be. It keeps what worked, improves what didn't, updates the graphics without changing the feel of the game, and adds more playable content. Fallout 2 does each one of these things to the 100th power.
Everything from the simplest frustrations of the original (like not being able to choose between punches and kicks while in melee combat) to more intricate improvements (like the addition of gear management screens for allied party members) has been addressed. All of this in addition to expanding on the already massive scope of the first game If Fallout was an entire planet then Fallout 2 is a whole galaxy. The idea of choices that resonate and create a butterfly effect is even stronger in this game simply due to the sheer size of the game. Not to mention the fresh content in it: new traits, new items, and more missions.
The only one misstep in the transition from 1 to 2 is that the ability to ask talking NPCs your own questions was canned rather than improved. Still, in its place you'll find a staggering amount of dialogue options. There are even more distinct differences between playing a male vs a female character this time around.
Appropriately, the unofficial community support for Fallout 2 is equally fanatical with even more possibilities at your disposal. No Mutants Allowed Online and Killap's unofficial patches have fixed nearly all of the thousands of bugs and crashes that would have realistically docked from Fallout 2's overall score when it came out about ten years ago. Not only that, but the amount of content that has been cleaned up, finished, and added back into the game with those unofficial patches is nothing short of jaw-dropping. It's not an exaggeration to say that playing Fallout 2 today with these patches is simply a better, more complete experience than had you played it back in the day.
What Fallout 2 gains from having such a gigantic world, it has to sacrifice a little in terms of overall narrative...but not much. It still deals with and earns the M rating with its political and sexual subtexts as well as its sometimes bleak, sometimes funny ponderings of mankind...not to mention its gloriously bloody battle system. Fallout simply had an epic storyline that shadowed almost every action made in its expansive world. Fallout 2 has a sprawling storyline that unfolds in different directions, but reaches the same ending point. There's a perfect balance of paying homage to and following up on the events of the first while confidently defining itself. The in-jokes and references (particularly the returning characters) for veterans of the first are wickedly clever. Of course the actual content of the finale depends infinitely on your choices as a player and a character.
There are some sequels that are simply a cash-in bashed on a brand that's already been established. There are some sequels that try, but just can't recapture the feeling of the original.
Fallout 2 makes no compromises and is not even one shred less legitimate than the original. If it took ten years for someone to exhaust all the possibilities of Fallout, then Fallout 2 would take twenty. Even more importantly: if you loved the original, it is impossible not to love this followup.