ΔE 30.7, loose: different enough that you should pick on purpose. Battle Mud Wash is noticeably lighter, more muted, warmer than Grove Hollow Shade.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 31). Battle Mud Wash is noticeably lighter, more muted, warmer than Grove Hollow Shade.
The same difference applies the other way round: Grove Hollow Shade 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 Grove Hollow Shade on the colour wheel See Battle Mud Wash on the colour wheel
All matches: Grove Hollow Shade equivalents · Battle Mud Wash equivalents