all games are not created equal

A bigger world, more characters, and a huge number of things to do makes Fallout 2 much better than Fallout.  When it comes to sheer amounts of replayability as well, Fallout 2 takes the cake. Both games are great, but the sequel has improved on the original in many ways.

You're thinking, why compare these two games? The answer: replayability and game length. Lumines  is fun for a puzzle game, and will likely addict you for a few hours. But in the end, you're doing the same thing over and over again. In Fallout 2, however, the world is constantly introducing new characters, locations, and challenges. Thanks to the level of character customization, you can also create a variety of playthroughs, each one different than the last. It's the reason people keep coming back to Fallout 2, while Lumines merely falls back to the wayside as 'that PSP puzzle game that was pretty popular in the past'.

I've loved the Fallout games since Wasteland.  Yes, I consider Wasteland as part of the Fallout universe and will still play it with DOSBOX occasionally.

I can not say enough good things about Fallout 3, really.  You can complain if you wish that there aren't a HUGE load of quests to do, but that doesn't mean that there isn't much to do at all.  There's so many small civilizations to see, including the Citadel, Rivet City, Megaton, Little Lamplight, Big Town, and The Republic of Dave.  The characters all have good voice acting, although you'll hear the same voices repeated many times through different characters (ESPECIALLY with the Brotherhood of Steel). 
The weapons are fun and look fantastic (I love the shishkebob myself) and give you plenty of chances to gore people.  VATS works wonderfully, while the real-time action leaves some to be desired.

Fallout 2 had a great story, and also a great land to explore.  You met a couple characters from Fallout 1 for nostalgia sake, but everything else was terrific.  Enemies were interesting and exploded if you poked them with a spear, and the quests had you dealing with some puh-retty interesting people.  Also, at one point you get a car that lets you travel across the map and skip the annoying random encounters you normally put up with.

However, Fallout 2 didn't improve on Fallout 1 as much as people had hoped.  For one, the game was pretty hard.  It wouldn't be uncommon for someone to save after every single encounter with an enemy.  Also, the random encounters became tedious, and the final encounter felt uninspired and seemed pretty tacked-on.  It wasn't at all as epic as The Master from Fallout 1.
Fallout 3 failed to deliver on epic encounters, however.  You don't really have much for bosses, though there ARE behemoth mutants scattered very friendly, and the deathclaws are probably one of the most nerve-wracking enemies you'll ever encounter in a game, period.  There is so so much detail put into the game that actually made it feel like a real world.  There is so many places you can go to that serve absolutely no purpose to the main story, but have their own background.
One of my favorite places in Fallout 3 is either vault 106 or 108 (I forget which).  It contained a cloning lab where you will fight many clones of a vault dweller named Gary.  It provided some pretty funny dialogue, but somehow made the place very creepy.

Anyways, both games are great so you really can't go wrong either way.