ΔE 16.0, loose: different enough that you should pick on purpose. Obsidian Black is noticeably lighter, more muted than Bright Gun Metal.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 16). Obsidian Black is noticeably lighter, more muted than Bright Gun Metal.
The same difference applies the other way round: Bright Gun Metal is noticeably darker, 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 Bright Gun Metal on the colour wheel See Obsidian Black on the colour wheel
All matches: Bright Gun Metal equivalents · Obsidian Black equivalents