ΔE 57.1, loose: different enough that you should pick on purpose. Sparkling Amethyst is noticeably lighter, much more muted, cooler than Royal Purple.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 57). Sparkling Amethyst is noticeably lighter, much more muted, cooler than Royal Purple.
The same difference applies the other way round: Royal Purple is noticeably darker, much 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 Purple on the colour wheel See Sparkling Amethyst on the colour wheel
All matches: Royal Purple equivalents · Sparkling Amethyst equivalents