ΔE 24.6, loose: different enough that you should pick on purpose. Royal Blue is a little lighter, more muted, cooler than Beaten Purple.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 25). Royal Blue is a little lighter, more muted, cooler than Beaten Purple.
The same difference applies the other way round: Beaten Purple is a little darker, 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 Beaten Purple on the colour wheel See Royal Blue on the colour wheel
All matches: Beaten Purple equivalents · Royal Blue equivalents