Incoming wall of text
as big as both ladies' oppai ovo
Irene has Enchantment, so she can probably buff her stats, so maybe AP and dura advantage for her.
IIRC in-character Irene spams explosions in a fight instead of transmuting, so that takes care of the most dangerous hax she has, transmutation.
Climate change can probably counter Ice Storm, but I'm not sure. Ice Storm is Esdeath's accumulated energy of several days released all at once and reaches Country. IDK if a Mountain level can fully counter it, but probably able to do so in a small area where they fight, not the entire empire that Esdeath's Ice Storm can cover. Uncertain for this weather match.
Now her most used attack is spammable explosions by enchanting the air. I don't know if Esdeath's perception and senses can sense changes in the air near her before explosions can occur. But if she can, then Ice Shield or Mahapadma to protect her. And it's not like she can't tank or dodge them. These explosions aren't like Killer Queen's. Although explosions certainly are helpful in dealing against Esdeath's ranged projectiles.
Possession is... also uncertain. Esdeath resisted her Danger Beast in the blood she drank's attempt to break her mind, although IDK if it can control someone's body after breaking their mind. Also Irene's possession worked so well when used on Wendy because Irene is familiar with Wendy's dragon slayer magic, so IDK if she would be willing to use it on someone she has zero knowledge about skills and how they work.
Don't remember how her teleport works. If it's spammable, then it's an advantage for her unless Mahapadma. Same as Fire Enchantment that I don't remember how it works. But then again, Esdeath's fire-resistant ice shields.
My biggest issue is Universe One. In-universe Irene used it to remove
the biggest player out of the battlefield and to collect the scattering Spriggan members together. So unless you are overwhelmingly stronger than her like Acno (which Esdeath isn't), I don't think she uses it in a one-on-one.
Now let's see what Esdeath can do:
As I said, ranged projectiles spam can be countered by explosions. But if it's the massive columns/ spikes/ boulders of ice, then they can do some damage even after having parts of it exploded. Though Irene can always make bigger explosions if that's the case.
Ice Armor can protect her from explosions.
Irene has no counter to Ice Entrapment unless she enchants herself strong enough to physically break free.
And finally, Mahapadma. Irene has no answer for that. Esdeath can activate it with a thought near-instantly. And considering her character, unless she is overwhelmed by explosions spam and the (questionably spammable) teleportation, she ain't using it soon. So inconclusive for this.
Finally let's talk about their skills and
personalities ( ͡° ͜ʖ ͡°). While both have spent years killing fodders (Irene's 400ish >>> Esdeath's at most 20 years), admittedly when you compare them without looking at the numbers Esdeath > Irene in pragmatic combats. PIS maybe, but Irene still had trouble fighting 2 girls whose combined ages is a fraction of hers. Both are also good at psychological attacks, but Esdeath is shown more resistant than Irene. The former never gives a shit unless it's Tatsumi, while the latter lost her cool when Erza sprouts her friendship stuff.
Sooo... after that massive wall of text, I say Esdeath with extreme difficulty