FAIII will always be an amazing game, but for me NV was a more enjoyable play; more interesting map with great locations, richer and fuller storyline(s), more varied missions, more choices and paths, far more different companions, better graphics (that green filter had been removed so the world looks less depressing), better atmosphere.

They are both good in their own way though; FAIII is supposed to be bleaker and darker, both visually and in terms of theme (like all the underground sections with the ghouls).
Cook the man some eggs!