To be specific, on Burst:
0 stars: nothing (like all Relic weapons)
1-2 star: -10% Def (Eidolon)
3 star: -25% Def (Eidolon)
Additionally, the Axe has +30 burst from using her third skill while also giving you 30% Elemental attack (each Soul has their own 30% Elemental attack weapon, so it's not specific to Hercules). 30% Elemental attack is amazing, not to mention that this lets you use Provisional Forest with no trouble, so it's just... stupid.
Meanwhile, The Bow boosts the damage of the first skill and increases damage cap to 1m. And 30% HP. Which is... okay, I guess? But why would you ever pick that over the Axe...?It pretty much NEEDED to be Assault or nobody would've used it. So it's good that they're going that route.
Also, odd that they went with Vritra. Water already had Rahab... meanwhile, Thunder and Wind are sitting at 0 FLB Advent events.