Compounds would be better described in terms of their aggressiveness at polishing, rather than actual grit size or fineness. The actual size of the grit won't necessarily determine how it finishes a particular steel. 'Green' compound, if it's pure, will usually be a very fine chromium oxide at around 0.5 - 1 micron in size. It's not very hard either, as compared to a 'white' compound (usually aluminum oxide). So, between green's small size and lesser hardness, it won't be as aggressive a polisher as will be the aluminum oxide.
Because aluminum oxide is harder than chromium oxide, its 'white' versions can be very aggressive polishers on steels with a little more wear resistance - these would be stainless steels like 420HC, 440A/C, 154CM, VG-10, etc. Even though a 'green' chromium oxide might be smaller ('finer') and less hard, it'll struggle to fully polish some of these steels - so it won't leave as fine a finish, if there are many coarse scratches in the steel.
'White' aluminum oxide compounds can vary more in size (I use one that's rated at 2-5 microns). But with moderately wear-resistant steels as mentioned above, it'll be a better polisher than will the green.
Green compounds will polish well with simple carbon steels (1095, CV, etc.), because those steels have much less wear resistance in the form of hard carbides that would otherwise be found in the stainless steels mentioned earlier.
Best way to evaluate how they work is just to use them. You might test them first on plain paper laid over your bare strop, so you can get a feel for how they fit in a polishing sequence. When you have a better feel for that, then you can go ahead and load your strop with your preferred compound.
For me, if I have a 'green' and a 'white' compound - I'd make my choices based on what steels I'm working with, as explained above. I wouldn't generally use both in a sequence however, as they both can produce similar results on their own when chosen for a specific steel based on its wear-resistance alone.