ΔE 17.9, loose: different enough that you should pick on purpose. Obsidian Black is noticeably darker, more muted than Bronze.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 18). Obsidian Black is noticeably darker, more muted than Bronze.
The same difference applies the other way round: Bronze is noticeably lighter, more saturated.
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 Bronze on the colour wheel See Obsidian Black on the colour wheel
All matches: Bronze equivalents · Obsidian Black equivalents