ΔE 22.8, loose: different enough that you should pick on purpose. Dwarven Gold is a little lighter, much more muted, cooler than Weapon Bronze.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 23). Dwarven Gold is a little lighter, much more muted, cooler than Weapon Bronze.
The same difference applies the other way round: Weapon Bronze is a little darker, 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 Weapon Bronze on the colour wheel See Dwarven Gold on the colour wheel
All matches: Weapon Bronze equivalents · Dwarven Gold equivalents