ΔE 18.1, loose: different enough that you should pick on purpose. Bronze is a little darker, much more saturated than Gun Metal.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 18). Bronze is a little darker, much more saturated than Gun Metal.
The same difference applies the other way round: Gun Metal is a little lighter, much 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 Gun Metal on the colour wheel See Bronze on the colour wheel
All matches: Gun Metal equivalents · Bronze equivalents