I just tested berserk. The character that has this ability will glow red and be "uncontrollable."
Useful for maps where you don't really care if you can control the character. I can see it being useful in situations like in porcelain tower when you run out of skills to use and using this for the attack boost and hp gain.
As far as I've observed in wikis of some FF games that have similarities on the definition of "Berserk", "Berserk" puts the unit into an uncontrollable state and is only restricted to use Normal Attacks. However, the units PA (Physical Attack) is increased by "x1.5", or rather a +50% damage boost.
-Note: This is only an assumption of mine based on other FF games.