ΔE 15.1, loose: different enough that you should pick on purpose. Piggy Purple Ink is a little lighter, warmer than Gothic Blue. They are different kinds of paint: Army Painter Gothic Blue is an opaque base/layer paint and Formula P3 Piggy Purple Ink is an ink, glaze or transparent paint, so they won’t behave the same on the model even where the colour is close.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 15). Piggy Purple Ink is a little lighter, warmer than Gothic Blue. They are different kinds of paint.
The same difference applies the other way round: Gothic Blue is a little darker, 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 Gothic Blue on the colour wheel See Piggy Purple Ink on the colour wheel
All matches: Gothic Blue equivalents · Piggy Purple Ink equivalents