ΔE 22.3, loose: different enough that you should pick on purpose. Dioxazine Purple is noticeably darker, cooler than Phoenician Purple.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 22). Dioxazine Purple is noticeably darker, cooler than Phoenician Purple.
The same difference applies the other way round: Phoenician Purple is noticeably lighter, 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 Phoenician Purple on the colour wheel See Dioxazine Purple on the colour wheel
All matches: Phoenician Purple equivalents · Dioxazine Purple equivalents