It should be noted that this question assumes HAM (amateur) radio jargon/conventions and in that context it is strange to compare CW (a "digital" communication modality used with morse code) to SSB (an "analog" strategy used with voice communication).
If you transmit a monotone signal (like morse code) using SSB modulation the effective signal in the air consists of only one frequency as well (assuming SSB-SC -- carrier suppression). That signal is offset from the carrier by its tone frequency, but there is still only one tone in the air.
Therefore, at a theoretical level this question is silly since you are talking about a single tone and whether you On-Off key (OOK) the carrier (CW), or offset a single frequency from this magical carrier (SSB-SC) and OOK that, is completely irrelevant. The same energy is in the air.
That is to say, if your CW carrier is 1MHz, the equivalent carrier for SSB-SC transmission of a 3kHz tone is 1.003 MHz assuming you use the lower side band. Both strategies result in an airborne transmission at 1MHz. So from physics, energy is proportional to frequency (given constant amplitude), the signal energy is exactly the same.
If you now expand the question to include the radio hardware that is generating/receiving the signals, OOK (CW) hardware is typically simpler and, therefore obviously, requires less quiescent and operational power.