Do energy of signal and power spectrum (in db/hz) indicate towards same signal property?
On a straight forward approach, energy of a signal given by $E = \int \limits_{-\infty}^{+\infty}|x^2(t)|dt$ is a constant number whereas PSD can be obtained from FFT which is a function of frequency. PSD is the square of the absolute value of FFT.

In either case the value of energy or PSD gives an insight of the amplitude/strength of a signal.