ΔE 18.8, loose: different enough that you should pick on purpose. Ultramarine Blue is a little darker, more saturated, cooler than Emperor's Purple.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 19). Ultramarine Blue is a little darker, more saturated, cooler than Emperor's Purple.
The same difference applies the other way round: Emperor's Purple 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 Emperor's Purple on the colour wheel See Ultramarine Blue on the colour wheel
All matches: Emperor's Purple equivalents · Ultramarine Blue equivalents