the probability of error is dependent on the quantity Eb/No usually the dependence is erfc(Eb/No), as the argument of erfc() increases , the prob. of error decreases, thus we need either high Eb or low No.
Eb/No is the SNR because Eb is the energy per bit for the clean signal and No is the noise PSD amplitude. The importance of Eb/No is thus of great importance and all BER and SER curves are plotted versus Eb/No.
I would say that in digital, you have the same piece of information throughout a bit duration, so you need the entire power that lasts through Tb; this is energy. But in Analog, information is instantaneous and Tb then tends to zero, thus we talk about power.