Why do people say an FX lens 'shines' more on FX than DX

Keeping the obvious focal length differences aside, I often hear/read where people say a lens (say the 70-300 VR) is good on DX but shines on FX. Wouldn't using an FX lens on DX let you use more of the sweet spot of the lens and possibly give even better results or at least equal?

I have both a D700 and a D40 and am planning to get the 28-300 VR and was wondering if I can expect similar results on both.