Esdeath scales to 1.58 Petatons due to naturally outputting a small percentage of her Ice Storm Commander In Chief, which is 250 Petatons
Gray scales to 2.2 Petatons naturally due to scaling at least to Base Wendy, while Devil Slayer Mark Gray scales vastly above 4.435 Petatons due to scaling to Base Natsu, who could 1 shot Enhanced Neinhart, who was so strong he could completely ignore Brandish, who is at that level
Gray should fold Esdeath in half without much difficulty even in Base, as despite them being rather close in power, Gray can literally eat all of Esdeath's attacks unless she gets in close, in which case Gray should overpower her in close quarters. His resistances and stamina replenishment should allow him to deal with Esdeath pretty easily
Ice Storm Commander in Chief seems to not be a massive AOE attack as far as I'm aware, so Esdeath isn't 1 shotting Gray with it, since it looks like she's just making a big storm, not hitting with the force of one, and if she does use it, then Gray can just... eat it constantly. Esdeath can constantly replenish her own stamina with it, while Gray continues eating everything. Both resist each others's ice, but Gray's resistance is better, he has access to Absolute Zero while Esdeath doesn't (and even if she did Gray still resists it), and he still smacks her harder than she smacks him.
Makahadoma is Esdeath's only wincon from what I can see, since Gray has no immunity to time stop, and he's not durable enough to just tank Esdeath's sword swings. The issue with this, though, is that unless Esdeath acts out of character, she's just gonna get cocky and stab Gray in the chest and call it a day, to which Gray responds by "power of friendship"ing through it as most fairy tail characters do (in actuality he just has insane stamina and has actually fought with broken bones and pierced organs before), and Esdeath just dies
so unless Esdeath goes for the head with time stop, Gray should win
Ive never actually watched Akame ga Kill so I'm not sure how exactly Esdeath fights so I'm gonna hold off on a vote for now tho