All of my tanks use sponge filters powered by submerged powerheads. They provide the same filtration as a HOB type filter. The output of the powerhead can be completely underwater, or you can direct it toward the surface of the water to make a ripple or splash if you want more aeration. You can also add air to the tank by an attachment. It can pull air from above the tank and mix it with the water it is circulating, acting almost like an airstone.
The powerhead draws water up thru a lift that has been pulled thru the sponge. The sponge collects debris and provides a surface for the bacteria to grow on. When the flow starts to get restricted, usually about once a month, I take the sponge off and squeeze it out in a bucket of used tank water to get some of the buildup off, just as you would with the HOB filter pads.
If you have fry or small fish, they will pick at the sponge and eat the infusoria that collects there. All of my sponges are split in two parts so if I need a new tank quickly, I just attach 1/2 of the 'old' sponge to the new tank's powerhead, and its cycled instantly.
The advantages of a sponge filter with a powerhead vs. a HOB filter to me include practically silent operation. All you have to do is make room for the cord to plug it in. Since my focus is on plants, I don't have to worry to keep the water level high on an HOB filter (more splashing of the water surface means more CO2 is offgassed, which is less food for my plants). I can let the water level drop for a few weeks due to evaporation, and then 'rain' new, colder water on the tank, which simulates the rainy season and induces many fish to spawn.