I'd be less concerned about the grit size, and pay more attention to how each will polish, and how crisp they'll leave the edge. If the rouge is aluminum oxide, it'll be a better, cleaner cutter of the steel than the green will be, even if the green's size might be finer. I've tended to favor the aluminum oxide white rouge, over green compound, for most mid-grade stainless steels with some wear-resistance (think: 440C, 154CM, D2, etc). For very simple carbon steels and low-alloy stainless (420HC, 440A, etc), green can work very well, and leave the edge very, very crisp. Green starts to falter a little bit with more wear-resistant steels, tending to burnish or round off the apex, because the compound itself (chromium oxide) is less hard than the carbides in those steels (chromium carbide, vanadium carbide in particular). That's where the aluminum oxide could do a better job refining the edge, even if it's grit size is somewhat larger.
A lot of 'jeweler's rouge' compounds will be intended for softer metals worked by jewelers (brass, gold, silver, copper, etc). That's to say, they are NOT formulated to cut hardened metals, like cutlery steel, very well. The 'white rouge' in those cases might be something like tin oxide, which is much too soft to be useful on steel. More aggressive compounds that work well to polish steel might be overkill or even damaging to the metals used by jewelers, especially on plated jewelry, on which the compound might strip the plating off in a heartbeat.
If this leather crafter was using the rouge for his cutting tools, that's a decent sign it may be an aluminum oxide compound. Give it a try on a blade in basic carbon steel (1095, CV) or low-alloy stainless (420HC, etc), and see how fast it polishes the bevels. Try it on a strop of denim or linen, for best effect. If you also notice the strop blackening with swarf very quickly, that's also a good sign it's aluminum oxide.
David