*Grinds skull into desk*
What part of "Original writers", Original developer team", and "Is LITERALLY the story they wrote for Fallout 3" Are you having trouble with?
New Vegas is Fallout 3. This is not debatable in any way shape or form, the head developers of the original two games have gone on record as saying that it is the Fallout 3 story they wanted to tell, the gameplay is different but gameplay does not a sequel make. A sequel is a continuation of an extant storyline within a defined setting, that is EXACTLY what New Vegas is to Fallout 1&2.
You claiming that NV is not Fallout 3 is factually incorrect according to the only people who matter, the people who created the Fallout setting. No game made within the last ten years is going to "feel" like games made a decade or more before, the methods of giving players information have changed so massively that the old text-based systems are starting to grate on even long-time gamers like myself. It's an FPRPG, and that isn't the way such games were made twenty years ago (well, some were, but it wasn't popular), but it was the only chance that the creators were ever going to get to make the game they had been wanting to make for over a decade. I'd further argue that Fallout 2 doesn't exactly "feel" the same as Fallout did, the world was much more populated, there were far more locations, the story was far more obfuscated and required much more investigation than Fallout. Using "feel" as an argument is pretty weak in this case, if you'd like to argue that it is very mechanically different and you don't like it that's fine, but your argument does not in any way change what the game is.
The camera perspective is not what makes a Fallout game, the gameplay mechanics is not what makes a Fallout game, being set in the Fallout setting is what makes a Fallout game, that is why the Bethesda games are not Fallout in any way shape or form, and NV IS.