ΔE 26.2, loose: different enough that you should pick on purpose. Beetle Green is noticeably darker, more saturated, cooler than Emerald Dimension.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 26). Beetle Green is noticeably darker, more saturated, cooler than Emerald Dimension.
The same difference applies the other way round: Emerald Dimension is noticeably lighter, more muted, warmer.
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 Emerald Dimension on the colour wheel See Beetle Green on the colour wheel
All matches: Emerald Dimension equivalents · Beetle Green equivalents