ΔE 19.4, loose: different enough that you should pick on purpose. Cobalt Violet Hue is more saturated, warmer than Phoenician Purple.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 19). Cobalt Violet Hue is more saturated, warmer than Phoenician Purple.
The same difference applies the other way round: Phoenician Purple is more muted, cooler.
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 Cobalt Violet Hue on the colour wheel
All matches: Phoenician Purple equivalents · Cobalt Violet Hue equivalents