ΔE 22.7, loose: different enough that you should pick on purpose. Omega Blue is a little lighter, much more muted, cooler than Arcane Purple.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 23). Omega Blue is a little lighter, much more muted, cooler than Arcane Purple.
The same difference applies the other way round: Arcane Purple is a little darker, much more saturated, 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 Arcane Purple on the colour wheel See Omega Blue on the colour wheel
All matches: Arcane Purple equivalents · Omega Blue equivalents