The Full Moons are the warriors and athletes and combat specialists of the Lunars. But there are more ways to fight than simply wading into your opponents, and more ways to achieve victory than through force of arms.
The value of Dexterity has been made clear to anyone who studies the combat system, and Full Moons receive a discount in purchasing all three Physical Attributes. It has been observed that putting freebies into attributes at character creation is one of the cheapest and best investments for Lunars.
The Anima ability for Full Moons improves their movement rates all around. See LunarsAreFine/CombatTactics for some discussions on the tremendous advantage that ground speed can impart in combat.
Charms From Favored Attributes
Full Moons strongly favor large parts of Unarmed Combat, Armed Combat, and Defense.
Lunars have two exceptional defense/counterattack Charms at their command: Snake Body Technique [prereqs: Sinuous Striking Grace, Body Weapon Technique] and Crouching Tiger Stance [prereqs: Feline Guard Technique, Steel Paw Style]. Both are Essence 2, meaning that even a basic starting Lunar can learn them, and both are based on Dexterity, which Full Moons favor. See LunarsAreFine/CombatDefenses for a discussion of the mechanical uses of these Charms.
What Lunars don't have is a lot of general-purpose reflexives that offer them some sort of defense. What they DO have are reflexives that provide great defenses UNTIL THEY TAKE AN ACTION. A Full Moon whose action comes around is expected to be doing something decisive about whoever his opponent is - either putting him out or running away. Within these limits, a Lunar who prefers dodges and parries to soak-regenerate strategies is perfectly viable. See LunarsAreFine/CombatDefenses for an overview of the defense Charms.
It's a mistake to assume that Full Moons make good generals - they don't. See LunarsAreFine/ChangingMoons for hints on Lunar leadership during wartime. What Full Moons are exceptionally good at is acting as independent heroes or duellists on the battlefield.
The Full Moon anima ability can make a Lunar champion exceedingly nimble, able to engage other heroes or units more or less at will. Most units Lunars will engage are going to be led by Dragon-Blooded, and a canny Full Moon who can duel and defeat a unit's commander (and any relays) can "kill" a unit quite swiftly, just acting alone.
A Full Moon is also an excellent choice for disabling or commandeering artillery - in a flying form they can get past any outer rings of security the artillery piece may have, and they can trivially clear out any mortal crews. And a Lunar can destroy any artillery that a mammoth could, by plowing into it as one.
Bodyguard or Sentinel
Needs expansion - don't have my book handy -- BillGarrett
There's always the fact that as a Lunar, you're one sentry that can be exceedingly hard to spot (having the Heart's Blood of a squirrel or hummingbird can work wonders for your ability to blend-in while at the same time keeping highly mobile) while patrolling, especially in overgrown areas like jungle or forest. Alternately, having a human form that's innocuous/appropriate for bodyguarding -- JadeSerpent
Lunars are the best bodyguards, as the Solars deserve. Note that they get anti-ambush Charms, anti-observation Charms, have Charms to both parry and dodge attacks for others, have a "heal someone else's wounds instantly" Charm, have a wide range of powerful Perception Charms, and oftentime require very little powerup time to bring their combat prowess into play.
Add that onto their ability to take any shape they wish, and you see why the Solars kept them around. -TheMyriadOfShades