ΔE 15.9, loose: different enough that you should pick on purpose. Imperial Purple is noticeably lighter, cooler than Permanent Violet Dark.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 16). Imperial Purple is noticeably lighter, cooler than Permanent Violet Dark.
The same difference applies the other way round: Permanent Violet Dark is noticeably darker, 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 Permanent Violet Dark on the colour wheel See Imperial Purple on the colour wheel
All matches: Permanent Violet Dark equivalents · Imperial Purple equivalents