Advantages? If you have many tanks, they can all be run off one central air pump powering all those sponge filters. That air pump will likely use less electricity than just one or two of the individual water pumps you would otherwise be using.
Sponges can handle very high bioloads, certainly higher than any other type of filter on a per-kilowatt-of-electricity basis. As stated above, they run practically for free if powered by air, especially a central air system. They weigh practically nothing when dry, are easy to clean, and require no expensive replacement elements.
If you are frequently starting new tanks, sponges allow an essentially instant cycle. Keeping a couple extra sponge filters running in other tanks, or perhaps in sumps, provides you with a sponge populated by a mature culture of beneficial bacteria that is easily moved to a new tank. Just add fish. I'm sure someone will pipe up that too many fish added at once might still overwhelm that filter's initial capacity; true enough. If you have a tank containing a certain bioload that is run by two sponge filters, then putting one of those into a new tank provides that tank with half the population of BB. You would need to install no more than half the bioload in the new tank to achieve absolutely no ammonia/nitrite spike, and might experience such a spike in the original tank as well since you have robbed it of so many BB. But...it will take no more than a couple days for the BB population to double if sufficient food is available to them. Meanwhile, cutting down food in the old tank for a few days, and minimal feeding (or none at all) in the new tank for a couple days pretty much eliminates this issue. Now, compare that to the alternative: weeks or months of dosing a tank with ammonia, and testing, testing, testing...all to arrive at the same end point, i.e. a fully cycled aquarium. When you read some of the threads here, where people are wringing their hands in worry because the fish they bought
that morning isn't eating yet...the fast approach has even more appeal.
Noise is a non-issue if you use airstones. Bare air lines can be noisy bubblers, so if you are sensitive to this, you will need to invest in an airstone for each sponge to keep that diabolical bubbling to an acceptable level.
Finally, and this is a subjective thing: some people like things simple. To them, the appeal of a sponge filter is obvious and undeniable. Others are happy to look for the complicated approach; to assemble as much high-tech hardware as can be fit into and around a tank. Those folks can still utilize sponge filtration, and just combine it with all the humming pumps, blinking lights, dosing devices and banks of valves. All that junk won't interfere with the sponge at all.
Edited to add:
Rocksor
beat me to it; he types fast and is concise. I don't and am not.