I've played them all, more or less as they came out, and the reasons I think more fondly on 1 & 2 are rather varied.
For the first part, there's the increased level of detail in character interactions. More dialogue options, particularly in Fallout 2, and VASTLY more options dependent on skills and attributes than you see in Fallout 3. There are quests you simply cannot do without the right perks, goals you can't achieve, etc.
Fewer rules in character interactions. Fallout 2 really shone in what it allowed the player character to do in this regard. I recall one of the blurbs for it at the time it came out was "Fall in love, get married, then pimp out your spouse for some extra chump change", and yes, that was indeed an option. Or you could get caught messing with the farmer's daughter, fail to talk your way out of it, be forced at gunpoint to marry her, take her to the Den and sell her into slavery, then go back and tell her father and watch him die of a heart attack.
And yes, I did that.
You could kill kids. Screw Fallout 3 and their wussing out on that issue, tossing nukes galore around Megaton but somehow children are immune. Is it a nice thing to kill kids? No, but it's certainly not any worse than tossing a nuke into your local bar & grill. In Fallout 2, for example, you got a huge penalty if you killed children, but it was an option. Alternately, of course, you could trick your followers into killing them for you, which had certain advantages.
The NPC followers, for the most part, had vastly more character than the ones in Fallout 3, and you could have more of them. It wasn't a one + dog situation, it was a "how many people can I keep around with my stats/skills?" situation.
On the down side, of course, the games were buggy as all hell, and if you knew what you were doing you could skip ahead to critical events, then go back and complete the rest of the game with relative ease, but still, the games just had more character than Fallout 3.