ΔE 21.8, loose: different enough that you should pick on purpose. Brown Grey Wash is a little lighter, much more muted than Mid Brown.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 22). Brown Grey Wash is a little lighter, much more muted than Mid Brown.
The same difference applies the other way round: Mid Brown is a little darker, much more saturated.
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 Mid Brown on the colour wheel See Brown Grey Wash on the colour wheel
All matches: Mid Brown equivalents · Brown Grey Wash equivalents