Why Fury is best on Eir

When she runs Fury 3, she takes 4 damage after combat. this is because she would take 10 due to her weapon, but Mythic boost 3 reduces it to 4 damage.

That being said, Fury is wonderful on her.

If you worry about her taking the 4 damage until she puts herself to 1 health, don't be. her weapon only damages her when she is above 50% health, so once she crosses that boundary, she stops taking the 4 damage.

Of course in order to make the best use of her, you need to keep her above 50% hp, lucky she has just the skill to do this.

Her C skill, Sparkling Boost, heals 10 damage to whoever has taken the most damage, except for herself. This is easily abused by units such as Micaiah, who can use her personal command --Sacrifice-- to fully heal Eir, than get healed by Eir's c skill. Micaiah also takes care of Eir's counters, armored units.
Just about any unit with ardent sacrifice will work amazingly with Eir.

You can also run Reciprocal Aid on her to make her completely self sustaining so long as she has an ally to bounce off of.
This can work great for units who run desperation, since she will swap her ~50% with them, than slowly heal them over a few turns, than swap again.

Fury is also better than swift sparrow considering her base stats. Her high res makes her perfect for mage baiting, however, running Swift Sparrow confines her into a purely offensive role. For the cost of 1 atk and 1 spd, Fury allows Eir to run both phases and increase her bulk.
Her weapons built in swift sparrow effect even works on both phases, so confining her to offense is ignoring half of her potential.

TLDR; with fury she does everything she did with swift sparrow and more.

I have attached my Eir below, the keen eye will find that I have hidden my friend code should you want it.