Grimdark Shadow vs Battle Mud Wash

How close are they?

ΔE 27.8, loose: different enough that you should pick on purpose. Battle Mud Wash is noticeably lighter, more saturated than Grimdark Shadow.

Can I use Battle Mud Wash instead of Grimdark Shadow?

Not as a straight swap; see the closer alternatives below. Loose match (ΔE 28). Battle Mud Wash is noticeably lighter, more saturated than Grimdark Shadow.

Can I use Grimdark Shadow instead of Battle Mud Wash?

The same difference applies the other way round: Grimdark Shadow 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.