ΔE 16.5, loose: different enough that you should pick on purpose. Dioxazine Violet is much more saturated, warmer than Broodmother Purple.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 17). Dioxazine Violet is much more saturated, warmer than Broodmother Purple.
The same difference applies the other way round: Broodmother Purple is much 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 Broodmother Purple on the colour wheel See Dioxazine Violet on the colour wheel
All matches: Broodmother Purple equivalents · Dioxazine Violet equivalents