Yes. Both are good. Aeration in the biological portion(s) of the filter assure high oxygenation for efficient nitrification, and can be set up to prevent/minimize settlement of fines, thereby promoting a healthier biofilm. But this is not the same as maximizing oxygenation of the pond where the fish are.
Let's say you have a 5,000 gallon pond and your aerated filter is processing the entire pond volume each hour. If no other aeration technique/device is in use. Water coming from the filter is theoretically at near-saturation and is entering the pond at a rate of less than 100 gallons per minute. Only a small percentage of water at the surface of the pond is in direct contact with the atmosphere. If the water is still, a thin film of oils will be on the surface impeding air exchange. If the water from the filter is returned so as to agitate the surface, the waves created can double, triple or quadruple the surface area exposed to the atmosphere, while breaking up the oil film.
A single bottom drain airdome, however, can be moving the entire volume of the pond to the surface every few minutes. Rather than an oxygenating turnover of 5,000 gallons per hour, the airdome can expose the entire pond volume to the surface within minutes... depending on the volume of air being pumped, shape of the pond, etc. But, this pond water will suffer some degree of oxygen depletion as it travels through the filter system. Aeration in the bio-filter addresses that challenge.
For the hobbyist there are compromises to be made. The more aeration and agitation that occurs, the less visible the koi.
In overstocked situations, visibility has to take a back seat altogether. I believe high oxygen levels are a major reason my koi have done well since building my current pond. With airdomes, aeration in the bio-chambers and a Bakki (an efficient waterfall), the several months they spend at water temperatures of 78F and higher are not as limiting as they once were.
Quote: 
05-25-2008
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