ΔE 21.8, loose: different enough that you should pick on purpose. Piggy Purple Ink is a little darker, more muted, warmer than Royal Robes. They are different kinds of paint: Army Painter Royal Robes is a one-coat contrast-style paint and Formula P3 Piggy Purple Ink is an ink, glaze or transparent paint, so they won’t behave the same on the model even where the colour is close.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 22). Piggy Purple Ink is a little darker, more muted, warmer than Royal Robes. They are different kinds of paint.
The same difference applies the other way round: Royal Robes is a little lighter, more saturated, cooler.
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 Piggy Purple Ink on the colour wheel
All matches: Royal Robes equivalents · Piggy Purple Ink equivalents