ΔE 34.8, loose: different enough that you should pick on purpose. Witch Purple is noticeably lighter, much more saturated, cooler than Emperor Red.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 35). Witch Purple is noticeably lighter, much more saturated, cooler than Emperor Red.
The same difference applies the other way round: Emperor Red is noticeably darker, 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 Red on the colour wheel See Witch Purple on the colour wheel
All matches: Emperor Red equivalents · Witch Purple equivalents