ΔE 21.6, loose: different enough that you should pick on purpose. Iridescent Bright Gold (Fine) is noticeably lighter, much more saturated, warmer than Hoard Bronze. They are different kinds of paint: Army Painter Hoard Bronze is a metallic and Golden Iridescent Bright Gold (Fine) is a pearl paint, so they won’t behave the same on the model even where the colour is close.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 22). Iridescent Bright Gold (Fine) is noticeably lighter, much more saturated, warmer than Hoard Bronze. They are different kinds of paint.
The same difference applies the other way round: Hoard Bronze is noticeably darker, much more muted, cooler.
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 Hoard Bronze on the colour wheel See Iridescent Bright Gold (Fine) on the colour wheel
All matches: Hoard Bronze equivalents · Iridescent Bright Gold (Fine) equivalents