ΔE 22.6, loose: different enough that you should pick on purpose. Xereus Purple is noticeably darker, more muted, cooler than Amethyst.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 23). Xereus Purple is noticeably darker, more muted, cooler than Amethyst.
The same difference applies the other way round: Amethyst is noticeably lighter, 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 Amethyst on the colour wheel See Xereus Purple on the colour wheel
All matches: Amethyst equivalents · Xereus Purple equivalents