ΔE 16.7, loose: different enough that you should pick on purpose. Dark Prussian Blue is noticeably darker, more muted than Amethyst Rayne.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 17). Dark Prussian Blue is noticeably darker, more muted than Amethyst Rayne.
The same difference applies the other way round: Amethyst Rayne is noticeably lighter, more saturated.
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 Rayne on the colour wheel See Dark Prussian Blue on the colour wheel
All matches: Amethyst Rayne equivalents · Dark Prussian Blue equivalents