ΔE 17.2, loose: different enough that you should pick on purpose. Dioxazine Violet is noticeably lighter, more saturated than Abaddon Black.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 17). Dioxazine Violet is noticeably lighter, more saturated than Abaddon Black.
The same difference applies the other way round: Abaddon Black is noticeably darker, 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 Abaddon Black on the colour wheel See Dioxazine Violet on the colour wheel
All matches: Abaddon Black equivalents · Dioxazine Violet equivalents