ΔE 13.9, fair: the same colour family, but not a straight swap. Emperor Gold is noticeably darker, more saturated than Burnt Metal.
Only where an exact match doesn’t matter, such as a new unit or a highlight. Fair match (ΔE 14). Emperor Gold is noticeably darker, more saturated than Burnt Metal.
The same difference applies the other way round: Burnt Metal is noticeably lighter, 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.
See Burnt Metal on the colour wheel See Emperor Gold on the colour wheel
All matches: Burnt Metal equivalents · Emperor Gold equivalents