ΔE 21.4, loose: different enough that you should pick on purpose. Old Rose is a little darker, more saturated, cooler than Burnt Umber.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 21). Old Rose is a little darker, more saturated, cooler than Burnt Umber.
The same difference applies the other way round: Burnt Umber is a little lighter, more muted, 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 Burnt Umber on the colour wheel See Old Rose on the colour wheel
All matches: Burnt Umber equivalents · Old Rose equivalents