ΔE 21.6, loose: different enough that you should pick on purpose. Deep Magenta is a little lighter, much more muted, warmer than Permanent Violet Dark.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 22). Deep Magenta is a little lighter, much more muted, warmer than Permanent Violet Dark.
The same difference applies the other way round: Permanent Violet Dark is a little darker, much more saturated, 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.
See Permanent Violet Dark on the colour wheel See Deep Magenta on the colour wheel
All matches: Permanent Violet Dark equivalents · Deep Magenta equivalents