ΔE 17.6, loose: different enough that you should pick on purpose. Castellax Bronze is noticeably lighter, more saturated than Emperor Gold.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 18). Castellax Bronze is noticeably lighter, more saturated than Emperor Gold.
The same difference applies the other way round: Emperor Gold is noticeably darker, 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 Emperor Gold on the colour wheel See Castellax Bronze on the colour wheel
All matches: Emperor Gold equivalents · Castellax Bronze equivalents