ΔE 18.5, loose: different enough that you should pick on purpose. Luxion Purple is noticeably lighter, warmer than Beowulf Blue.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 19). Luxion Purple is noticeably lighter, warmer than Beowulf Blue.
The same difference applies the other way round: Beowulf Blue is noticeably darker, 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 Beowulf Blue on the colour wheel See Luxion Purple on the colour wheel
All matches: Beowulf Blue equivalents · Luxion Purple equivalents