Okay, I'm going to tackle this one in traditional OrcishLibrarian style. In other words, I'm going to start with a baseless pop-culture analog, then proceed onward from there in a rambling stream of consciousness until I either arrive at a conclusion of run out of steam.
To paraphrase my favorite philosopher, Red Green: It's not smart, and it doesn't make sense. It's just the way I do this.
Okay, here's our obvious jumping-off point. Ashiok uses your own dreams to hurt you. So, for all intents and purposes, Ashiok is Magic's Freddy Krueger.
Now, that gives us a clear angle of attack on this problem. As long as Kiora and Sarkhan can just stay awake, Ashiok/Freddy can't hurt them. Which raises the logical follow-up question: Which of Sarkhan or Kiora is less likely to fall asleep?
Kiora, being of the crashing wave and all that, is probably at the greatest risk of being lulled into slumber by soothing ocean sounds. Therefore, one can logically conclude that she's going to eventually take a little nap, and is probably going to be gruesomely and ironically dispatched by some sort of nightmare kraken monster. Which leaves us with one down, and two to go.
Sarkhan is all about his dragon form. And dragons, being among the most metal of all mythical beasties are probably too busy rocking out to get much shuteye. (Except when they sleep on top of giant piles of treasure. Since, to the best of my knowledge, Sarkhan doesn't have such a treasure stash, I'm going to assume that he dodges this bullet.)
Anyway, I assume that Sarkhan dragons-up, put on his Beats, cranks the volume on "Operation Ground and Pound" up to 11, and headbangs the whole time while giving Ashiok an almighty whuppin'.
The final verdict: Ashiok defeats Kiora, Sarkhan defeats Ashiok, Ronnie James Dio rises from the dead and records a concept album about the whole thing.
Do we have evidence Ashiok needs people asleep in order to work? His known deeds, such as creating horrific two headed leonin, were done while the recipients were awake. Therefore, Kiora and Sarkhan can get insomnia and still get screwed.
I'm voting for Kiora because she has weird dreams and goals, so she can draw on her insanity to go Aracuan bird on Sarkahn and Ashiok.