I'll try to not get too into depth here.
Sintered glass biomedias (Eheim SubstratPro and what
@Willcooper is referring too by the round logs, Biohome Ultimate, more porous/surface area than ceramic media) is supposed to have the most surface area.
Though Cermedia MarinePure, which is made of inert aluminosilicate ceramic, has some pretty nice claims, but is expensive.
Seachem Matrix (smaller version would have more surface area for nitrifying bacteria than the larger sized Pond Matrix, but the Pond matrix does have *more potential space for denitrifying bacteria *when used in flow rates higher than 50 GPH) is another material with a large amount of surface area per volume. Regular Pumice stone may be the same thing (still not 100% confirmed) at a even cheaper price.
There are also open cell foams (poret foam, etc) that claim to have large amounts of surface area.
But there is also different nitrifying filtration methods that are can be more effective at nitrifying even without these biomedia that have large amounts of surface area per volume. Such as Fluidized/Moving Bed Filters (can use sand or many different light material such as K1 kaldnes and the likes), or Wet/Dry filters that provide a more oxygen rich environment for nitrifying bacteria.
As Willcooper hinted at, lava rocks looks very porous, but those "pores" don't tunnel network all through the internal structure of the material, so just the outside surface is really the only available surface area, while other materials really do have pores that allow water to pass through the internals (more surface available inside the media).
But as already mentioned early in this thread, if your current set up is working just fine, there is no need to change anything/upgrade (you can just use carbon or purigen as needed though). The Beneficial bacterial colonies will only grow to a population size to handle the given bio/nitrogen load. Large amounts of surface area can be unused if you don't have much bioload that would require all that space.
I'll throw a monkey wrench in, these highly porous biomedia with a large amount of surface area, the pores are really small and clog easily so when those pored clog, those water passageways are cut off, making the internal surface unusable for nitrifying bacteria (not enough oxygen reaching those areas, but does provide a suitable environment for denitrifying anaerobic bacteria so that can be a plus if desired), so it pretty much negates the purpose of using those high surface area biomedias.
