ΔE 23.3, loose: different enough that you should pick on purpose. Emperor's Children is noticeably darker, much more saturated than Gum Pink.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 23). Emperor's Children is noticeably darker, much more saturated than Gum Pink.
The same difference applies the other way round: Gum Pink is noticeably lighter, much more muted.
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 Gum Pink on the colour wheel See Emperor's Children on the colour wheel
All matches: Gum Pink equivalents · Emperor's Children equivalents