Looking at Harbor Freight's description of each, the blue is described as:
and the green described this way:"Multi-shine polishing compound for high-gloss shine on plastics, gold, silver, and die-cast items."
This suggests to me, the blue compound likely isn't very aggressive on steel, regardless of how fine the particle size may be. It's intended for use on soft metals and plastics, so it's probably pretty soft. Might not have much effect at all, on steel. I probably wouldn't bother with the blue compound on a strop."SSX compound achieves a high-polish finish on copper, brass, stainless steel, and steel.
(Edit: Looking around at other vendors' descriptions of 'blue' compounds, they all seem to suggest it's not a cutting compound at all, on metals. It doesn't abrade metal, so it can't sharpen steel, presumably.)
Green compound is almost always chromium oxide, which is a good polisher for hardened steel, at a (typically) smaller particle size around ~0.5 microns, on average. Use this on the strop; it'll likely do better.