ΔE 21.4, loose: different enough that you should pick on purpose. Emperor Gold is noticeably lighter, much more saturated than Burnt Iron.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 21). Emperor Gold is noticeably lighter, much more saturated than Burnt Iron.
The same difference applies the other way round: Burnt Iron is noticeably darker, much 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 Iron on the colour wheel See Emperor Gold on the colour wheel
All matches: Burnt Iron equivalents · Emperor Gold equivalents