That's what makes discussion about these two games so interesting. I thought Fallout 3 had far more memorable moments. I can still recall some of them, while the more recent NV fails to stick with me as much. I found many of the NV quests to be more tedious than rewarding.
Doesn't mean we didn't enjoy both games, but our preferences certainly do vary.
first of all, i've spent >250 hours in fallout 3, so i clearly had a lot of fun with the game, and i'll be buying 4 for sure, whoever will be involved in its development.
still, as somebody who has played the first two fallouts, that blatant copy-pasting of story pieces from these games was incredibly annoying, and quite an immersion breaker for me.
but i like sandbox games, and a sandbox game in a post-apocalyptic environment, with a lot of attention to detail and an arguably better weapon balancing than new vegas has, is hard to dislike, even with a crap, copied story, and with a few exceptions, very flat and boring characters.
the writing of characters and dialogue in new vegas is lightyears beyond what was offered to us in part 3.
new vegas feels way more like a living, believable world, than fallout 3 did.
3 never left the explore-kill-loot formula with always hostile acting npcs outside of settlements, and while i also can enjoy that quite a bit, it is rarely enough to create what i would define as a great moment for me.
some people would call a random encounter between an enclave patrol, some outcasts, 2 albinos and couple of raiders a great moment, for me thats just funny, not more, not less.
a great moment, thats for instance, as mentioned above the dialogue you're having with boone in "i forgot to remember to forget", especially around and shortly bitter springs. that was really something, that touched me a bit, something that rarely happens to me in video games.
or go to camp searchlight with a lvl 7 character, if you want have real struggle for survival in a superbly dense atmosphere, you could never have that in fallout 3. such things are, what i would call great moments, but as tastes differ, so do personal definitions of terms