The single most important distinction is between what purity measures — the fraction of detected material that is your target — and what you actually want to know — how much of the material in the vial is your target.
Gradient slope controls resolution, and gentler slopes resolve co-eluting impurities into separate peaks — so the better method reports the worse purity number.
To be exact about it, tailing factor measures peak shape, and a badly tailing peak spreads into the region where small impurities live, forcing tangent-skim integration that assigns tail area to the main peak.
Published side-by-side method comparisons show that a two-point difference in purity on the same vial is easily explained by method choice alone.
Worth noting that method standardisation is poor in the research-grade space compared to pharmaceutical work, so identical-looking methods can produce different results.
Compare purity within a single laboratory on the same method, never across laboratories.