ΔE 13.5, fair: the same colour family, but not a straight swap. Azurite Hue is more muted, cooler than Royal Robes. They are different kinds of paint: Army Painter Royal Robes is a one-coat contrast-style paint and Golden Azurite Hue is an opaque base/layer paint, so they won’t behave the same on the model even where the colour is close.
Only where an exact match doesn’t matter, such as a new unit or a highlight. Fair match (ΔE 14). Azurite Hue is more muted, cooler than Royal Robes. They are different kinds of paint.
The same difference applies the other way round: Royal Robes is more saturated, warmer.
ΔE is the colour difference between our two swatch estimates: under about 6 is close, over about 15 is loose. Real paints also differ in finish, coverage and how they thin, so test before you commit.
See Royal Robes on the colour wheel See Azurite Hue on the colour wheel
All matches: Royal Robes equivalents · Azurite Hue equivalents