Hi, Air stones are almost entirely aesthetic. To understand this, it is important to understand the basics of 'aeration'.
Almost all 'aeration' occurs at the water surface. Here, the carbon dioxide in the water is swapped for oxygen from the atmosphere. The larger the surface area of the water, the more gaseous exchange can take place. This is beneficial as fish and nitrifying bacteria like a high oxygen saturation.
If the surface of the water is agitated, water which otherwise wouldn't have been at the surface is pushed up to the surface. This water is then oxygenated by the gaseous exchange at the surface before being pushed back down to allow other water to come up. This effectively increases the surface area of the water. ie. all of the water in the tank can then be oxygenated constantly.
If no surface movement occurs, then only the water on the surface can take in oxygen and the rest of the water will become stagnant.
Very little oxygenation occurs on the surface of bubbles rising through the water, although when these bubbles reach the surface, they agitate the surface slightly and have the desired effect, all be it quite limited. Some people like the aesthetic effect of an airstone and this tends to be the main reason for having air stones in the aquarium, although they do have a limited capacity for oxygenating the water.
A powerhead is capable of much more surface agitation than an air stone, by pushing much more water to the surface, and is therefore the most effective for the purpose. If you already have adequate surface agitation, neither a powerhead or air stone is required, although neither would do any harm. If the surface of the water is constantly rippling, this should be adequate.
This applies regardless of whether the filter is cycled.
Hope this helps.
