ΔE 32.4, loose: different enough that you should pick on purpose. Emperor's Children is noticeably lighter, more saturated, cooler than Burnt Offering.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 32). Emperor's Children is noticeably lighter, more saturated, cooler than Burnt Offering.
The same difference applies the other way round: Burnt Offering is noticeably darker, 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 Burnt Offering on the colour wheel See Emperor's Children on the colour wheel
All matches: Burnt Offering equivalents · Emperor's Children equivalents