For me, it comes down to the vibe and atmosphere. Fallout 3 feels post-apocalyptic. Style-wise, they nailed it.
New Vegas is bright and colorful. Never gave me a feeling of fear or dread.
You could try playing DUST Survival Simulator
It’s basically a total game overhaul, and instead of quests; the only objective is to survive.
Made by the same mod author, there’s DUSTy Weather which only adds the weather effects from DUST without all the gameplay changes. There’s also Apocalyptic Mojave which adds more raiders to the world and fortifies existing settlements. Those two combined are essentially a budget DUST, they bring the apocalyptic feel that you’re looking for, but keep almost everything intact.
Just shop around for mods until you’ve made a combination that you like.