Triumphant Navy vs Bad Bruise

How close are they?

ΔE 16.1, loose: different enough that you should pick on purpose. Bad Bruise is much more muted, warmer than Triumphant Navy.

Can I use Bad Bruise instead of Triumphant Navy?

Not as a straight swap; see the closer alternatives below. Loose match (ΔE 16). Bad Bruise is much more muted, warmer than Triumphant Navy.

Can I use Triumphant Navy instead of Bad Bruise?

The same difference applies the other way round: Triumphant Navy is much more saturated, 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.