ΔE 41.4, loose: different enough that you should pick on purpose. Ancient Copper is noticeably darker, much more muted, warmer than Rhulic Gold.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 41). Ancient Copper is noticeably darker, much more muted, warmer than Rhulic Gold.
The same difference applies the other way round: Rhulic Gold is noticeably lighter, much 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 Rhulic Gold on the colour wheel See Ancient Copper on the colour wheel
All matches: Rhulic Gold equivalents · Ancient Copper equivalents