All those materials (including something as simple s lava rock) are simply surfaces for beneficial bacteria to grow on.
One may have more surface area than another, providing in theory (more area, so more good bacteria).
But bacterial populations coincide with the amount of ammonia, and nitrite produced by the stocking of fish. Fewer fish, less ammonia, many fish. more metabolism byproducts.
So with any media, if your ammonia, or nitrite spikes, then you need more or maybe better media (or more water changes).
If it remains stable, you probably don't, unless you add more fish.
If you don't regularly clean the gunk out of your media, and it gets plugged up with debris, it doesn't matter how much surface area you have. Beneficial bacteria are aerobic, so if covered with gunk, they don't function as efficiently.
If you mechanically filter out debris before the bio-media, you may not need to clean it as often.
I use lava rock as bio-media, I can get a barrel full for under $10, and I often use 50 gallon barrels as sumps filled with it, and mechanically filter the effluent with filter socks to prevent the bio-media from muddying up.
