Depends upon some factors.
Q: Does Abeloth have endless supply of bodies?
Q: Does Emperor Vitiate have endless supply of bodies?
Abeloth is typically reckless in her decision-making in combat related matters. Emperor Vitiate can destroy her avatar(s) from a reasonable distance, thanks to his own great power and superior mastery of the Force.
Setting may also come in to play. Emperor Vitiate can use the surroundings to his advantage to crush avatars of Abeloth, he is a brilliant tactician. I don't recall Abeloth's use of surroundings to her advantage much often but she has sufficient power to use a favorable setting to her advantage if she thinks wisely and does not makes reckless decisions.
I can see either side winning in some battles but stalemate in the long run.
Abeloth was powerful enough to beat down the Son and Daughter at the same time. And either of them alone are more powerful than Vitiate. Vitiate has never done anything close to the destructive level of the devastation of Tahv without prep or a ritual, and is not a dozen times stronger in the force than FOTJ Luke.
As far as recklessness goes, let's not forget that Vitiate is the guy who walked into a lightsaber blade, and turned his attention away from one of the people trying to kill him, leaving himself exposed to a killing blow while taking his sweet ass time walking over to Revan.
As far as tanking though, Abeloth has tanked a lightsaber blade through the chest with no effect to her, while Vitiate fell to the floor clutching his side when the Hero slashed him.
The official Star Wars blog confirms that, despite the implications of the Killik murals, Abeloth is lesser than the Mortis Anchorites.
The architects had a stepmother of sorts named Abeloth, a being similar, but not quite as powerful as the Celestials. Unfortunately, Abeloth had been driven mad in a bid for power, and for the good of the galaxy, would have to be imprisoned.
Either way, she stomps.
Originally posted by Emperordmb
As far as tanking though, Abeloth has tanked a lightsaber blade through the chest with no effect to her, while Vitiate fell to the floor clutching his side when the Hero slashed him.
This is what makes me side with Abeloth. I believe Vitiate would be able to demonstrate equally powerful force attacks but would fall short while defending. He is very well capable of defending himself against extremely powerful attacks no doubt but he is not immune as much as Abeloth