In particular, SiC (black) and aluminum oxide (white) can be very aggressive polishing media, especially on simpler steels like 1095 and 420HC, etc. A distinction needs to be made, in that some of these compounds won't remove big, coarse teeth on very wear-resistant steels in a hurry, but they will still aggressively polish what is there. In other words, they can quickly refine the edges & tips of the teeth, as well as the valleys in between them. At the actual apex of the edge, that can make all the difference. SiC compound in particular can remove the teeth from a 320 or higher-grit edge pretty fast, if taken too far on a steel like 1095 or 420HC (this comes from my doing so on Case's 420HC stainless, as well as on CV and 1095). I use 600-grit SiC on balsa to remove heavy wires/burrs that otherwise won't be fazed by something like green compound or bare-leather stropping. And the SiC can quickly polish and over-polish these edges in doing so, if I take it too far.
So, in other words, if perfectly mirrored bevels are the goal, these compounds can't do it all by themselves; they need the proper prep ahead of time. On the other hand, if enhancing the cutting characteristics of the edge itself is the objective, they can quickly make all the difference. After all, it's the apex that makes it sharp or not; mirrored bevels won't help if that isn't done first. It's not so much about how much metal the compound removes as a whole, but the scale at which it can make the most significant difference.
David