Most deisgned ceramic media (such as Fluval biomax) contain a higher amount of surface area per volume than sponge through small hollows through the material as well as the non-smooth surface.
With filter media it is a trade off. The more surface are per volume, the larger area for bacterial colonisation, but you then find yourself at the point where the media gets clogged up very quickly, thus reducing how effectively it hosts bacteria.
Bioballs are a fantastic source of high surface area, but without good mechanical filtration they will clog up very quickly. That is why most large filters have different stages of filtration (and why it is fine to rinse purely mechanical filtration under the tap).
for mechanical filtration, the smaller the route through the media, the more physical waste will be removed, but obviously it will have to be cleaned more often. I use filter floss on my wet dry towers as it removes almost all of the detritus, however it needs rinsing off far more often than a sponge would.