ΔE 26.2, loose: different enough that you should pick on purpose. Emperor's Children is noticeably darker, more saturated, warmer than Cold Pink.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 26). Emperor's Children is noticeably darker, more saturated, warmer than Cold Pink.
The same difference applies the other way round: Cold Pink is noticeably lighter, 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 Cold Pink on the colour wheel See Emperor's Children on the colour wheel
All matches: Cold Pink equivalents · Emperor's Children equivalents