ΔE 15.1, loose: different enough that you should pick on purpose. Brown Rose is noticeably darker, cooler than Rosy Shadow.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 15). Brown Rose is noticeably darker, cooler than Rosy Shadow.
The same difference applies the other way round: Rosy Shadow is noticeably lighter, 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 Rosy Shadow on the colour wheel See Brown Rose on the colour wheel
All matches: Rosy Shadow equivalents · Brown Rose equivalents