Thanks for the link Hektor. I don't have much technical experience to make a claim if the sample comparison was fair. The comparison between the two made the D800 appear to be cleaner.
However, if both files were printed on an A3 or A4 picture, the D800 might look cleaner since it tends to conceal the noise in the shadows better due to its larger file size. That is just my assumption based on what was previously explained to me.
With that said, I wonder how will the D800 fair against the D4 if you print the pictures and do a comparison at ISO 6400.