I don't think that there is a specific "effect." I think the D700 is amazing but I also think that a role of Ilford Pan F Plus is equally amazing or even more amazing.
Back to the topic. I see a clear (read: CLEAR) difference between my old dinosaur D100 and the D700. I am hesitant to ascribe it to the "FX effect" though as the D100 is the only other Nikon digital that I've used. I've never used the state-of-the-art D300 or D7000.
My decision to go back to FX was that I wanted to interchangeably use lenses between my F5 and the D700 without having to worry about the crop factor. With the F5, I had gotten so used to the 35mm projection angle of my lenses that using the D100 never satisfied me in that regard. I never liked that my 50mm became a "75mm." I never got used to the crop factor, I never acquired any DX lenses and I always hoped that at one point there would be a reliable FX sensor.