ΔE 21.7, loose: different enough that you should pick on purpose. Agrax Earthshade is a little darker, much more muted, warmer than Military Shade.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 22). Agrax Earthshade is a little darker, much more muted, warmer than Military Shade.
The same difference applies the other way round: Military Shade is a little lighter, much 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 Military Shade on the colour wheel See Agrax Earthshade on the colour wheel
All matches: Military Shade equivalents · Agrax Earthshade equivalents