If I HAD to choose only one, that would be tough. I like New Vegas better by far, but I think the nod here goes to Fallout 3 because it has some overlap with Fallout 4 such as Three Dog/GNR and the Institute/androids story arcs. But honestly, if you are at all interested in Fallout 4 then I can't see not playing both, even if you play New Vegas after Fallout 4.
I still recommend searching out Gopher's modding videos on Youtube for both games. If you are only going to play through once, why not make it as stable, bug free, and beautiful as possible? You're talking probably over a hundred hours to finish the main game, the DLC, and the side quests, and visit all the little nooks and crannies, so spending a few hours optimizing the game just makes sense. The mods I recommend include FWE (Fallout 3 Wanderer's Edition), Mart's Mutant Mod, Fallout Interoperability Program, the User Interface Organizer with Darnified UI/aHUD/iHUD, Fellout or Project Reality with Enhanced Weather for weather, the Large Address Enabler, Stutter Remover, and Fake Fullscreen for stability and performance, NMC's texture pack for beautifying everything, Weapon Mod Kits and CALIBR and EVE for more enjoyable weapons and weapon effects, Project Beauty and Fallout Re-Animated for prettier and more natural people, and of course FOIP, FOEdit, the Nexus Mod Manager, and the Fallout Script Extender to make it all work together. Here's the start:
https://www.youtube.com/watch?v=-SAeXsA6Nt8
One caveat here - for Fallout New Vegas I recommend playing through the early levels to get the story, then starting a new game using Project Brazil and kicking back into Goodsprings after Brazil's conclusion to start the
Ain't that a kick in the head main quest. I found Goodsprings to be weak compared to the writing in the rest of the game, Brazil leaves you with some back story rather than starting life getting shot in the head, and you start out in Goodsprings much better equipped which gives you a lot more freedom of movement in the early levels. (Assuming you are playing with difficulty-enhancing mods; vanilla Fallout New Vegas, like Fallout 3, is too easy even on the hardest difficulty.)