For me, it's about the politics (or lack of) in a post nuclear World.
The consequences also play a large part and the World Building.
All three I consider to be lumped into one group, the classics and New Vegas built around these components rather fittingly.
The stories are very much human, and about the damage that man can do.
Personally, I see the Fallout series itself not as a Post-Apoc series, but as a tale or rebirth and righting the wrongs. There is very much a survival element in them. New Vegas showed that sometimes the best options weren't exactly good, but needed to survive the Wasteland (you create your own personal fiction in that game, which is one of the reasons I love it so much).
One of the issues I have with 3&4 is how they miss out on these rather simple ideas and themes.
Fallout 3 was such a mess thematically that by the end, I had to question whether this was a human conflict.
It was just a simple tale of Greed, which we've seen a billion times over again.
As many people have said, Humour plays a big part.
One of the things that could have made F3 better was if Eden was an idiot, or a poorly programed A.I that just gave up on a second's notice.
Hell, even a one-off remark from Autumn could have saved the character of Eden.
But no, Bethesda understands the skin of Fallout, but not the layers.
In all honesty, Fallout is a series without good guys, or even bad guys for that matter.
The Master wasn't evil, he was a more justifiable Hitler in a World that needed something different.
The Enclave... fine, they are evil, yet as Arcade Gannon said in New Vegas "There were some good people in the Enclave".
Caesar's Legion isn't even that evil, just very flawed.
But Bethesda try to simplify that.
All of a sudden, the Brotherhood of Steel are good guys, even through they were never really shown to be in 1,2 or New Vegas (they then ended up being weird chaotic good in F4 however).
The Railroad are somewhat Wasteland saints.
The Institute are very bad.
The Minutemen are just laughable...
So to me, a good Fallout game is something that just feels real.
I'm not asking for hard actual science, just something that fits in the boundaries of its own Fiction.