Gothic Blue vs Beaten Purple

How close are they?

ΔE 20.7, loose: different enough that you should pick on purpose. Beaten Purple is much more saturated, warmer than Gothic Blue.

Can I use Beaten Purple instead of Gothic Blue?

Not as a straight swap; see the closer alternatives below. Loose match (ΔE 21). Beaten Purple is much more saturated, warmer than Gothic Blue.

Can I use Gothic Blue instead of Beaten Purple?

The same difference applies the other way round: Gothic Blue 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.