I have seen various powerheads used to run sponge, box and even canister filters. They work just as well as the airpump/airstone system.Air pumps offer far more than bubbles. Centralized air pumps are often used to create suction through sponge media.
I will argue with this. While air pumps do use less power per amount of water moved than the old impeller powerheads, the new bladed powerheads from Sunsun, JCB, and Korilina (Maybe others I don't know) are more efficient than air pumps. It is hard to get a straight answer for how much water a sponge filter moves, but if you google "airlift pump efficiency" you can get some equations and stuff to not only optimize your sponge filters and get the most out of them, but also see what the best they can do is. I will admit that I did the numbers looking at diaphram and piston style air pumps, maybe the more efficoent, larger and noisier centrifugal blower pumps will beat bladed powerheads. Again, the new JCB and Sunsun (I think they are the same) can be cheaper than air pumps.And air pumps are cheaper and use less power.
I will admit that the good old fashioned sponge and box filters that run off compressed air are simple, elegant and reliable. I have run tanks on contraptions made of oxygen mask tubes, soda bottles, bits of pvc and an air pump, using an old shirt as mech and packing peanuts and gravel as bio. If you have the air pumps, you can hack together legit filters out of garbage, and they work as well as any other.