ΔE 20.9, loose: different enough that you should pick on purpose. Imperial Gold is noticeably darker, more saturated, warmer than Ancient Gold.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 21). Imperial Gold is noticeably darker, more saturated, warmer than Ancient Gold.
The same difference applies the other way round: Ancient Gold is noticeably lighter, more muted, 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 Ancient Gold on the colour wheel See Imperial Gold on the colour wheel
All matches: Ancient Gold equivalents · Imperial Gold equivalents