A given compound, of a given abrasive type and grit size, will work effectively 'finer' on a softer strop of wood, leather, etc. than it would work in a hard-bound 'stone' of the same exact grit type & size. The difference is with the 'bedding' (substrate) into which the grit is embedded. Hard substrates will prevent or minimize the 'give' under pressure, which makes the grit dig deeper into the material being ground/polished; a softer substrate will have more give, in effect providing a cushion or 'shock absorber' under pressure exerted, which makes the grit work less aggressively.
In a nutshell, stropping with a particular grit type & size should enable more refinement, as compared to using the same identical grit in a stone. A real-world example is with DMT's EEF diamond: as used in their EEF hone (3µ grit; steel-backed and embedded in nickel substrate), it'll leave a coarser scratch pattern than the same grit used in DMT's 3µ Dia-Paste compound used on a strop of wood or leather, which produces a much higher polish.
And 'better refinement' sort of depends on what's meant by 'better' or 'refined'. The stropping compounds will certainly provide higher polish, all other things being equal. But, 'better refinement' could also imply a crisper edge with more 'bite', produced with a similar grit in a fine stone. Best way to know which is really 'better', is to try each and see which result suits you best.
David