Everything I discuss here will generally have a very small impact on gameplay, but could be the difference between winning and losing an arena match or getting hundreds of thousands more kills while farming over an extended period of time. That being said, I want to share my findings regarding the mechanics of the various branch damage types and which types of skills benefit the most from each branch.
Aal - skills that hit once with no multiplier, ex. 750%
When damage is calculated off of a flat value, Aal simply increases the damage.
Labreve - skills that hit once with a multiplier, ex. 250%x3
When damage is calculated with a multiplier, it will only count as a single "hit" on the target, but each segment of the multiplier has a separate chance to crit. Therefore, increasing the critical hit chance with Labreve is optimal.
Ahib - skills that hit multiple times, ex. 200% max 5 attacks
When damage occurs as a series of attacks, each attack has a chance to activate the "extra damage" granted by Ahib, giving skills with multiple attacks the highest potential benefit from this branch.
Serrett - optional use for farming or mass pvp
This branch is most useful in contexts where your adventurer will be taking on many targets at once.
Because the optimal option is not always available for certain skills, here is a list ranking the effectivity of each branch under each type of skill:
Skills that hit once
Skills with a multiplier
Skills with multiple attacks
I hope you find this helpful!