Both sentences are correct but mean different things. "Aren't you still hungry?" (Means I am surprised that you don't want more food. Maybe because you were really hungry [past] but you only ate a little bit and you don't want more food. So now I say this because I am surprised.) "Aren't you hungry yet?" (Means I am surprised you aren't hungry. Maybe because you have not eaten for a long time and you are still not hungry. So now I say this because I am surprised. Sometimes I say this when I am impatient to eat but my friends are not ready to eat yet.)

If you are expressing surprise that a person is not hungry because perhaps it's been a long time since that person ate: You're not hungry yet? You're still not hungry? If the person is eating and you are asking if they are still hungry after eating what you gave them: Are you still hungry?