According to Sheila Khosla's FFXI Summoner Guide, found at http://www.gamefaqs.com/computer/doswin/game/16968.html
New Moon: Ecliptic Howl gives 1 Accuracy and 25 Evasion.
50% Moon: 13 Acc, 13 Evasion
Full Moon: 25 Acc, 1 Evasion
Check out the guide for a full table of values for all moon phases, for Lunar Cry, Ecliptic Growl, and Ecliptic Howl.