ΔE 23.0, loose: different enough that you should pick on purpose. Arcane Gold is noticeably darker, more saturated than Battle Axe Brass.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 23). Arcane Gold is noticeably darker, more saturated than Battle Axe Brass.
The same difference applies the other way round: Battle Axe Brass is noticeably lighter, 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 Battle Axe Brass on the colour wheel See Arcane Gold on the colour wheel
All matches: Battle Axe Brass equivalents · Arcane Gold equivalents