The most important parameter is the one that is almost never specified: the gradient slope during the region where your main peak elutes.
Acetonitrile is the organic modifier of choice because it has a good UV cutoff, a reasonable viscosity and a refractive index that minimises baseline noise.
Specifically, system suitability checks on replicate injections of a known standard establish whether the method was in control — if the peak area varies by more than two per cent between replicates, something is wrong.
Inter-laboratory studies using identical methods on identical material show precision well within half a per cent when the method is locked down, pointing to method variability as the primary source of disagreement.
The caveat is that HPLC is a purity technique and says almost nothing about whether the main peak is actually your target compound — that is why identity confirmation from mass spectrometry or peptide mapping matters.
If two labs give different numbers, the method difference is the first hypothesis, not lab quality.