ΔE 21.8, loose: different enough that you should pick on purpose. Royal Purple is more saturated, warmer than Beowulf Blue.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 22). Royal Purple is more saturated, warmer than Beowulf Blue.
The same difference applies the other way round: Beowulf Blue 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 Beowulf Blue on the colour wheel See Royal Purple on the colour wheel
All matches: Beowulf Blue equivalents · Royal Purple equivalents