ΔE 26.6, loose: different enough that you should pick on purpose. Gloomy Violet is noticeably darker, much more muted than Luxion Purple.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 27). Gloomy Violet is noticeably darker, much more muted than Luxion Purple.
The same difference applies the other way round: Luxion Purple is noticeably lighter, much 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 Luxion Purple on the colour wheel See Gloomy Violet on the colour wheel
All matches: Luxion Purple equivalents · Gloomy Violet equivalents