ΔE 18.0, loose: different enough that you should pick on purpose. Balthasar Gold is a little darker, much more saturated, cooler than Burnt Metal.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 18). Balthasar Gold is a little darker, much more saturated, cooler than Burnt Metal.
The same difference applies the other way round: Burnt Metal is a little lighter, much 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 Burnt Metal on the colour wheel See Balthasar Gold on the colour wheel
All matches: Burnt Metal equivalents · Balthasar Gold equivalents