ΔE 15.5, loose: different enough that you should pick on purpose. Crimson is a little lighter, more saturated, warmer than Blood Thorn.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 16). Crimson is a little lighter, more saturated, warmer than Blood Thorn.
The same difference applies the other way round: Blood Thorn is a little 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 Blood Thorn on the colour wheel See Crimson on the colour wheel
All matches: Blood Thorn equivalents · Crimson equivalents