ΔE 20.3, loose: different enough that you should pick on purpose. Ancient Copper is noticeably lighter, more muted, warmer than Metallic Brown.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 20). Ancient Copper is noticeably lighter, more muted, warmer than Metallic Brown.
The same difference applies the other way round: Metallic Brown 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 Metallic Brown on the colour wheel See Ancient Copper on the colour wheel
All matches: Metallic Brown equivalents · Ancient Copper equivalents