I played through FO3 and all the expansions/DLC, and New Vegas (without DLC, because I bought it and played through it before they had released any), and never really got very far in the first two fallouts, but I liked New Vegas much more than FO3.
I'm in completely the same situation. I will add however that FO3 is worth it if you can get it cheap. It's not a BAD game per se (just like Oblivion wasn't BAD game, but...top RPG of the decade? Seriously??) and I don't mind the money I spent on it, but I wouldn't recommend buying GOTY if it isn't on at least 75% sale. Hey, some people have kids to feed (not me though). Anyways, I can't add much more than it has already been said, but I will try to expand on some comments.
First, the story: Some people argue the story in FO3 is better than in NV. The main reasoning I saw for this is because you (should) feel more emotionally connected to your character, because you start as a baby AND your father is an important actor in the story. The other reasoning is because you do something that heavily influences the surrounding area. Personally, I think the story suffers heavily from "Messiah complex". This isn't obvious from the start, but I think the ending definitely proves it. Mind you, this does NOT mean the story is forgettable - hey, some people enjoy this kind of setting and there's nothing wrong with it. On the other hand, why some people consider NV's story "bad" is because you start as a blank page - you know nothing about yourself, no name, no home, no past. And from the start, your missions is more or less just a grudge, payback type of mission. Now, here's where, personally, I disagree with this being bad, in fact I think this is absolutely great! It feels a lot more personal tracking someone down and trying to figure out just what is going on and being tabula rasa just adds to role-play potential. And as whole, I find the story a lot more engaging - instead of being led on more or less fixed path that is FO3's story, your story has a center idea, but you have a lot more options how to approach to it or even ignore some parts.
Second, equipment: NV wins here hands down. Not trying to play favorites here, but there's just more weapons and armor in NV and even weapon mods. But I also feels like stuff is more useful in general. Sure there are still high-tier weapons like minigun and rocket launchers, but there being more stuff means that even what is considered "bad" weapons (like pistols) get more advanced versions that are fully capable of being end-game weapons. Could you play a handgun oriented character in FO3? Hardly. But simply because there wasn't any end-game handgun in FO3.
Third, characters: the "problem" of NV's characters is they just feel more part of the world in general. I'll explain why in next paragraph but let's just say NV has people that simply work at being in NV's world. And I personally never understood why do people find FO3's Three Dog even remotely interesting. Like, at all. I remember hearing this before I started playing FO3 and when I finally met him he left me completely cold. And even his radio messages? Dunno, if anything, it sounded like he's trying too much to the point of being annoying.
Forth, the world and world building in general: Now, I think this is an important thing to note this is something these games do completely in the opposite way. And, very simply put, it's like that: FO3 build on the world's past. NV builds on the worlds present/future. What it means is that, one has to admit, FO3 does a lot better job of creating the illusion of a devastated world. You'll find messages on rusty, dusty terminals. Written on walls. Old mails, forgotten in suitcases. Voice logs. All describing either the coming doom or the actual moment itself. You'll find brittle skeleton on some forgotten toilet booth, clutching a rifle in a very obvious "barrel-in-the-mouth" suicide position. Two adult skeletons clutching around a child-like one on a family bed. Skeleton in bath, covered in pills. Decades old emergency shelters, littered with empty food cans and left in disarray that tells of the last, frantic struggle to survive in post-apocalyptic wasteland. Yes, FO3 paints a bleak, dead world that is nonetheless very interesting to delve into. However, this deadness makes much less sense when you realize how alive it really is. Or rather, how NV's world just feels more logical. See here, Mojave wasn't hit that hard by the nukes. Sure, you'll find devastated scenery and even radioactive puddles here and there. Not so post-apoc grim and bleak, for sure, as in FO3. But at least you actually see people growing food here. You see just WHY people would survive. Everything makes sense. Personally? I think FO3's world is one big them park. Lot's of things to discover, lot's of things to see. But if you want living world? NV's makes sense. And because things are where they should be (towns that grow food -> towns that trade -> towns that provide entertainment), so are the people also. There's let things to remind you of just HOW or why the people are living in such conditions but I'll be damned if NV doesn't at least make you actually care for them. I feel like I'm rambling at this point though and I would do better to include some actual example. But this would make this already long rambling even less bearable.
And don't get me started on DLCs. Well, nothing really to say, FO3's aren't that bad, really. Like the original game. But imho NV's worldbuilding is just better, again.
tl;dr - NV feels more alive in a meaningful way, FO3 has more stuff to find. NV in general also just feels more polished. An upgrade to FO3? Maybe, but a damn good one. Still buy FO3 one day if you can get it cheap somewhere.