I can't even remember half the characters or stories in 3, but distinctly remember many from New Vegas. In terms of the world and exploration, I feel like Fallout 3 was more densely packed, but I also thought New Vegas' felt more authentic and fun to explore. It made more sense and each location was more interesting than FO3 where it felt kind of slap-dash a lot of the time (endless metro tunnels, abandoned buildings etc).
I feel like Bethesda gave themselves a template and tried to do as much as they could with the template, and I think it paid off with their writing and level designs. You really don't know what you're getting into walking into a dungeon in Fallout 3. Could it be infested with ants? More ghouls? Maybe an underground Super Mutant stronghold? Groups of Raiders? Maybe some people hiding out? Bethesda gets a lot of shit for bad writing, but really that's only ever in the main quests. Their side quests, I find, are usually a lot of fun and well written, at the very least they're entertaining.
New Vegas tried to do a lot of different things without a template, and either failed to provide anything interesting, or ran out of time to finish it.
In New Vegas, the side quests I just felt were uninteresting, bland, and had boring characters. If they weren't making you trek across the desert (damn you Boomers), they were making you wander around and do a lot of, well, nothing. The main quest was a friggin' slog in New Vegas. I will praise the writing and acting up and down, but it was just so BORING. No matter what path you take, you get the platinum chip, activate the securitrons (though I think NCR skips that part), and then do a series of side quests you'd probably do anyway, and did I mention I find the side quests boring? After that, you get one interesting mission with the President of NCR, then go flip a switch, go to Hoover Dam, and the game is over.
In Fallout 3, you explored a derelict Vault, entered a simulation run by a 200 year old madman, rescued children from slavers, followed a giant robot around, repaired a radio station, escaped the enemy base (and optionally
blew up the President of the United States), and then it actually continued, provided you have DLC(which you'd honestly be stupid not to at least get that one nowadays. I'd forgive you if you skipped the rest). Even if the writing fell apart, it was loads of fun and had a ton of variety. I do not count "go do some side quests" as variety, that's just lazy.
It might help I played 3 first, but I honestly expected New Vegas to blow me away and become my new favorite, I was totally open to that. But it didn't, and I genuinely hope we get some traditional Bethesda flair in this new game.