ΔE 18.6, loose: different enough that you should pick on purpose. Ancient Gold is a little darker, much more muted, cooler than Castellax Bronze.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 19). Ancient Gold is a little darker, much more muted, cooler than Castellax Bronze.
The same difference applies the other way round: Castellax Bronze is a little lighter, much more saturated, 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 Castellax Bronze on the colour wheel See Ancient Gold on the colour wheel
All matches: Castellax Bronze equivalents · Ancient Gold equivalents