ΔE 17.4, loose: different enough that you should pick on purpose. Brown Wash is a little darker, much more saturated than Grimdark Shadow.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 17). Brown Wash is a little darker, much more saturated than Grimdark Shadow.
The same difference applies the other way round: Grimdark Shadow is a little lighter, much 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 Grimdark Shadow on the colour wheel See Brown Wash on the colour wheel
All matches: Grimdark Shadow equivalents · Brown Wash equivalents