ΔE 29.1, loose: different enough that you should pick on purpose. Violet Hint is noticeably darker, more saturated, warmer than Battleship Grey.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 29). Violet Hint is noticeably darker, more saturated, warmer than Battleship Grey.
The same difference applies the other way round: Battleship Grey is noticeably lighter, 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 Battleship Grey on the colour wheel See Violet Hint on the colour wheel
All matches: Battleship Grey equivalents · Violet Hint equivalents