ΔE 18.7, loose: different enough that you should pick on purpose. Emperor's Children is a little darker, more saturated, cooler than Old Rose.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 19). Emperor's Children is a little darker, more saturated, cooler than Old Rose.
The same difference applies the other way round: Old Rose is a little 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 Old Rose on the colour wheel See Emperor's Children on the colour wheel
All matches: Old Rose equivalents · Emperor's Children equivalents