ΔE 23.5, loose: different enough that you should pick on purpose. Crimson is noticeably darker, more saturated, cooler than Dusty Rose.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 23). Crimson is noticeably darker, more saturated, cooler than Dusty Rose.
The same difference applies the other way round: Dusty Rose is noticeably lighter, more muted, 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 Dusty Rose on the colour wheel See Crimson on the colour wheel
All matches: Dusty Rose equivalents · Crimson equivalents