ΔE 19.3, loose: different enough that you should pick on purpose. Dark Prussian Blue is a little lighter, much more muted, cooler than Dioxazine Purple.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 19). Dark Prussian Blue is a little lighter, much more muted, cooler than Dioxazine Purple.
The same difference applies the other way round: Dioxazine Purple is a little darker, much more saturated, warmer.
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 Dioxazine Purple on the colour wheel See Dark Prussian Blue on the colour wheel
All matches: Dioxazine Purple equivalents · Dark Prussian Blue equivalents