ΔE 29.0, loose: different enough that you should pick on purpose. Crimson is noticeably darker, much more saturated, warmer than Emperor's Children.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 29). Crimson is noticeably darker, much more saturated, warmer than Emperor's Children.
The same difference applies the other way round: Emperor's Children is noticeably lighter, much 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 Emperor's Children on the colour wheel See Crimson on the colour wheel
All matches: Emperor's Children equivalents · Crimson equivalents