ΔE 23.4, loose: different enough that you should pick on purpose. Battle Mud Wash is noticeably lighter, more muted, warmer than Athonian Camoshade.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 23). Battle Mud Wash is noticeably lighter, more muted, warmer than Athonian Camoshade.
The same difference applies the other way round: Athonian Camoshade is noticeably darker, more saturated, cooler.
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 Athonian Camoshade on the colour wheel See Battle Mud Wash on the colour wheel
All matches: Athonian Camoshade equivalents · Battle Mud Wash equivalents