ΔE 20.0, loose: different enough that you should pick on purpose. Martian Orange is noticeably lighter, more saturated, warmer than Crimson.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 20). Martian Orange is noticeably lighter, more saturated, warmer than Crimson.
The same difference applies the other way round: Crimson is noticeably darker, more muted, 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 Crimson on the colour wheel See Martian Orange on the colour wheel
All matches: Crimson equivalents · Martian Orange equivalents