So, I did some calcs, and if I did it right, with bonfire, Cherche gets +16 points of damage added to her attack, but with Dragonic Aura, she gets 16.5, which should round up to 17 then. Now, that's with Death Blow. Does Dragonic Aura could the buff from Death Blow when it procs? Because if so, then Dragonic Aura is slightly better than Bonfire. I'm very close to finishing Cherche, just need to figure out her special. Basically, I'm asking if Dragonic Aura takes Death Blow into consideration when it procs.
Draconic Aura does take death blow into consideration, but it does more damage overall to do death blow with bonfire, as it does 1 more point of damage. I did the damage calculations with a brave axe + in the damage calculator against neutral hector, and had the special proc on first hit. Draconic aura did 30 damage, while bonfire did 31 damage. overall, marginal difference, but go with bonfire.
Yes, Draconic does take Death Blow into account. But it rounds DOWN to 16 not up to 17, meaning they both do the same.
As for which one is better, it's situational. On the initiation, it depends solely on which buffs (or debuffs) she receives. If she gets Hone, Draconic is better, but if she gets Fortify, then Bonfire is better. Due to this reason, Draconic is generally better since Hone Attack is more common and useful than Fortify Defence.
On the enemy phase however, Bonfire is always more reliable since Cherche doesn't get Death Blow damage added and instead requires Hone Flier to do the same damage as Bonfire.
Hope this has helped.
Edit: From personal experience, I use Draconic with Hit and Run or if she's on my Flier Emblem (Since she gets 1 Hone and 2 Goads), Bonfire when she has Axebreaker so she can also bait, and Luna when doing PVE stuff.
So just give her both in my opinion, they're both relatively common to summon.
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