Does CW or SSB consume more power?
Your question suggests an actual use (that is, "pass a message on ARES"), so you've got to consider bandwidth as well.  Not so much how much band space you will occupy, but how long you'll be on the air.  How long does it take to send a message on CW vs. reading it on SSB?  Transmit time will affect the battery as much as the indicated power level.