ΔE 24.6, loose: different enough that you should pick on purpose. Crimson is noticeably darker, much more muted, warmer than Carmine Dragon.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 25). Crimson is noticeably darker, much more muted, warmer than Carmine Dragon.
The same difference applies the other way round: Carmine Dragon is noticeably lighter, 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 Carmine Dragon on the colour wheel See Crimson on the colour wheel
All matches: Carmine Dragon equivalents · Crimson equivalents