I'd say it depends on the type of leather it is, what steel(s) @ what HRC('s), what your intention is for stropping, and what sort of edge you're looking for...
I personally like stropping on horsehide after I finish sharpening on stones. Horse-butt leather contains more natural silicates than most leathers, as well as being very firm and tough. The feel of the edge against the strop tells me how well I've done at deburring, and improves the shaving ability ever so slightly without destroying the micro-teeth from my stones. It works well on carbon steels; less so, on high-HRC PM steels with lots of tungsten and or vanadium, like HAP-40, SG-2 / R2, CPM-S30V, etc... Even on very hard steels with lower carbide volumes, like Aogami Super or ZDP-189 @ 65+ hrc, it has some tiny effect, but not much... I like stropping my knives on this unloaded horse-butt strop before they start properly dulling, but are just only starting to lose that 'fresh' edge; before use, or before putting them away. It seems to help maintain that 'fresh off the stones' edge just a bit longer, with little or no metal removal... The effect of a bare horse-butt strop can actually be quite profound on very soft carbon, or stainless knives. 'Enthusiastic' usage on a Swiss Army Knife (SAK), or an old Sabatier can actually restore a mildly dulled edge to shaving sharpness without adding any extra abrasive compound, but the result does tend to be smooth, and not very toothy. It's also very useful on Mora's, for routine touch-ups while woodcarving.
Normal cow hide doesn't have that same effect. It tends to be too soft, easily rounding very slim edge bevels on well thinned knives (Even without compound.), and really needs compound to have much sharpening effect... On convex, or insanely steep edge bevels (Like those crazy 3-dps or so edges that Akifusa's shipping, these days.) it works, though.
I don't tend to be a big fan of CroX for culinary edges outside of maybe those intended for fish, herbs, or very fine garnish work... They're sharp, but even just a few strokes can kill the bite that most kitchen knives need. Even then, I prefer 0.5-micron or finer diamond.
1-Micron diamond paste is sort of a sweet-spot; especially Norton, as it has a wider grit spread (Normally a negative feature, but for food prep tends to be a positive on gyuto and such.). It'll restore mildly dulled edges on just about any steel, and has a good blend of shaving sharpness and tooth for food prep. Any finer, unless you're making a BIG grit jump (Like up to 0.1 micron or finer, for just a few strokes; just to help clean up a slightly ragged edge from a coarser stone.), and the edges just tend to get too smooth.
If you're stropping because you're in a "My knife is dull, and I'm in the weeds!" sort of situation, I'm becoming a fan of the JRE Black Compound... It's not great on the really high tungsten/vanadium steels (CPM-M4, S30V, S90V, etc.), but it'll get even moderately dulled knives up to SRS-15 and R2 licked back into shape within about 20-strokes either side (If it needs more, it's time to hit a 1K or coarser stone.), and leaves an edge with some good bite. It's also cheap...
For compounds, I tend to prefer 'hard' balsa (Sounds like a contradiction in terms, but there's different densities of the stuff. The type used for model airplanes, sold at craft stores, is just too soft.) to avoid edge-rounding; at least on compounds 1-micron and coarser. The natural silicates in balsa tend to leave random coarser scratches deeper than 0.5 micron, that ruins the polish. For finer compounds than than 1-micron, I prefer leather.
This is just my experience. Hopefully it helps.
