What does energy of the difference between two DFT's $X$ and $Y$ being 0 tell us about their corresponding signals $x$ and $y$?
If the energy of the difference is zero, than the difference is zero as well
If the difference is zero, than the signals are identical
Two signals with the same power spectral density can be completely different. A simple example: both white noise and a delta impulse have the same power spectral density