As I was picking which skill to unlock for my Navarre, I decided to do a little math on it on whether Killing Edge or Wo Dao would be better and since I do not want to lose this data, I decided to post it here in guise of helping others who may be interested. Anyway, here's the result of it.

Take into account first a unit with 30 Atk against an opponent with 30 Def.

Killing Edge will boost to 41 Atk. Wo Dao will boost to 43 Atk.

The result is obviously in favor of Wo Dao Moonbow due to Wo Dao's bonus Moonbow's trigger speed. However, is Moonbow the only good special for Wo Dao/Killing Edge? Here is a trial math with Luna(as if enemy suffered -50% Def/Res).

Since Luna purposely gimps Wo Dao's 10 damage due to a higher trigger cooldown, it loses out a lot of damage. On the other hand, Killing Edge gains damage due to the difference in recharge speed-to-damage ratio of the Specials on a 30 Defense target.

Let's have another example, this time using a Special that boosts Atk instead.

Wo Dao wins due to Draconic Aura scaling heavily to the Atk stat and is still fast enough in trigger time to make heavy use of Wo Dao's 10 damage and while Killing Edge still does lower damage, it enjoys the nice boost of attack due to being able to quickly use Draconic Aura.

Finally, using a skill that has a skill trigger time of 4 or more.

Killing Edge gets its most damage due to a heavy-hitting Special with a big discount in trigger time; while Wo Dao does get a good damage-per-action, the time it takes to prep up the special may take a toll in real battle.

To compare each weapon using all the given Specials:

tl;dr: Wo Dao is superior to Killing Edge overall but should always be coupled with a 2 or 3-action cooldown Special since it hits diminishing returns heavily as it relies on its 10 damage on trigger for a bulk of its damage. On the other hand, Killing Edge is more flexible and can be put to low-cooldown Specials for spamming or high-cooldown Specials for more damage-per-action.

For specials, Moonbow/Luna have varying degrees of effectivity since the bonus damage it gives is directly proportional to the Defense/Resistance of the enemy. ie. the higher the Defense/Resistance stat of the enemy is, the bigger the damage-per-action bonus of both these Specials give; the opposite applies as well. On the other hand, Draconic Aura/Dragon Fang give bonuses depending on the character's stats which are more stable to compute.

Finally, I would also like to say that this is all theoretical and that mileage may vary in actual practice. ie. even if a set-up has higher damage-per-action, it does not mean that it is, and will be, the best set-up in actual practice. To this, I would suggest never to put a 4 to 5-cooldown special alongside Wo Dao regardless of the damage-per-action it produces due to the innate gimping it produces by relying solely on normal damage.

Now that I think about it, I can see why various heroes with Killing Edge-esque weapons get Rising-type specials.