If you view an image at a standard size from both the FX and DX parts of an FX camera, you have had to magnify the DX capture more than the FX capture. So any noise at the pixel level is magnified too, even though the pixels are the same size.
Dynamic range is the difference between the lightest and darkest tones in an image. Because noise comes in random colours, noise makes the lightest tones darker in DX compared with FX, and the dark random noise means your tone is less bright. Similarly the darkest tones are a bit lighter in DX compared with FX for the same reason, because of the white noise in this case. So in DX, the range between white and black is lower - usually about 1 stop of exposure different.