The determining factor in attainable sharpness for a given substances is attainable hardness which is determined by carbon content in steel, and by grain-refinement, accomplished through specific alloying elements and HT. Blue#2 and White#2 have the same carbon content, but Blue's tungsten (W) content allows for a more refined grain = sharper edge at same hardness, and more abrasion resistance in that edge = Superior. White#1 & Blue#1 have higher carbon content than the previous 2 but the same principles apply, and Super Blue has even more carbon with grain-refiners and carbide formers to support the matrix = even higher attainable hardness with same grain-size and increased carbide content = higher attainable sharpness and abrasion resistance.
THAT is what the composition tells you - White steel canNOT achieve higher sharpness than Blue unless comparing White#1 to Blue#2. Now that might not make a difference if you can't actually achieve that superior sharpness in your sharpening - the steel doesn't automatically have that sharpness, you still need to get it there through proper equipment and technique, THAT is the limiting factor. A good maker using White#2 might achieve a thinner, longer-lasting edge than a lesser maker using Super Blue.
Regarding ease of sharpening, this again depends on equipment and technique. Using harder/sharper abrasives (e.g. diamond, SiC), the abrasives are so much harder than the steel-matrix, with or without carbides, that it takes no longer to abrade away the metal from one vs another. With inferior equipment, you may experience a difference in sharpening the resistant material vs the weaker one.