ΔE 18.5, loose: different enough that you should pick on purpose. Doomfire Magenta is a little darker, more muted, cooler than Carmine Dragon.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 18). Doomfire Magenta is a little darker, more muted, cooler than Carmine Dragon.
The same difference applies the other way round: Carmine Dragon is a little lighter, more saturated, 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 Carmine Dragon on the colour wheel See Doomfire Magenta on the colour wheel
All matches: Carmine Dragon equivalents · Doomfire Magenta equivalents