ΔE 20.6, loose: different enough that you should pick on purpose. Crimson is noticeably lighter, more saturated than Dark Magenta.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 21). Crimson is noticeably lighter, more saturated than Dark Magenta.
The same difference applies the other way round: Dark Magenta is noticeably darker, more muted.
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 Dark Magenta on the colour wheel See Crimson on the colour wheel
All matches: Dark Magenta equivalents · Crimson equivalents