ΔE 15.4, loose: different enough that you should pick on purpose. Battledress Brown is noticeably lighter, more saturated than Shadow Black.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 15). Battledress Brown is noticeably lighter, more saturated than Shadow Black.
The same difference applies the other way round: Shadow Black is noticeably darker, more muted.
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 Shadow Black on the colour wheel See Battledress Brown on the colour wheel
All matches: Shadow Black equivalents · Battledress Brown equivalents