Permanent Violet Dark vs Amethyst

How close are they?

ΔE 32.2, loose: different enough that you should pick on purpose. Amethyst is noticeably lighter, more saturated, warmer than Permanent Violet Dark.

Can I use Amethyst instead of Permanent Violet Dark?

Not as a straight swap; see the closer alternatives below. Loose match (ΔE 32). Amethyst is noticeably lighter, more saturated, warmer than Permanent Violet Dark.

Can I use Permanent Violet Dark instead of Amethyst?

The same difference applies the other way round: Permanent Violet Dark is noticeably darker, more muted, 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.