ΔE 16.5, loose: different enough that you should pick on purpose. Ultramarine Blue is noticeably lighter, more muted, cooler than Royal Burgundy.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 16). Ultramarine Blue is noticeably lighter, more muted, cooler than Royal Burgundy.
The same difference applies the other way round: Royal Burgundy is noticeably 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 Royal Burgundy on the colour wheel See Ultramarine Blue on the colour wheel
All matches: Royal Burgundy equivalents · Ultramarine Blue equivalents