ΔE 24.9, loose: different enough that you should pick on purpose. Medium Magenta is noticeably darker, much more saturated, cooler than Emperor's Children. They are different kinds of paint: Citadel Emperor's Children is an opaque base/layer paint and Golden Medium Magenta is an ink, glaze or transparent paint, so they won’t behave the same on the model even where the colour is close.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 25). Medium Magenta is noticeably darker, much more saturated, cooler than Emperor's Children. They are different kinds of paint.
The same difference applies the other way round: Emperor's Children is noticeably lighter, much 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 Emperor's Children on the colour wheel See Medium Magenta on the colour wheel
All matches: Emperor's Children equivalents · Medium Magenta equivalents