ΔE 22.9, loose: different enough that you should pick on purpose. Arcane Gold is a little darker, much more saturated than Chaos Bronze.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 23). Arcane Gold is a little darker, much more saturated than Chaos Bronze.
The same difference applies the other way round: Chaos Bronze is a little lighter, 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 Chaos Bronze on the colour wheel See Arcane Gold on the colour wheel
All matches: Chaos Bronze equivalents · Arcane Gold equivalents