These two exclamations can be used similarly or differently depending on the situation. But in general 에이씨 sounds stronger and more harshly than 아이구. They say 에이씨 with foul language in a terrible quarrel. But you can speak 에이씨to yourself to express your frustration.
For example, if your laptop doesn't work, you might say "에이씨, 이거 왜 작동안하는거야?"