ΔE 18.5, loose: different enough that you should pick on purpose. Brown Grey Wash is much more muted than Athonian Camoshade.
Can I use Brown Grey Wash instead of Athonian Camoshade?
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 19). Brown Grey Wash is much more muted than Athonian Camoshade.
Can I use Athonian Camoshade instead of Brown Grey Wash?
The same difference applies the other way round: Athonian Camoshade is 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.