ΔE 16.7, loose: different enough that you should pick on purpose. Amethyst Rayne is noticeably lighter than Broodmother Purple.
Can I use Amethyst Rayne instead of Broodmother Purple?
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 17). Amethyst Rayne is noticeably lighter than Broodmother Purple.
Can I use Broodmother Purple instead of Amethyst Rayne?
The same difference applies the other way round: Broodmother Purple is noticeably darker.
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.