Bright Red vs Cardinal Purple

How close are they?

ΔE 21.3, loose: different enough that you should pick on purpose. Cardinal Purple is noticeably darker, cooler than Bright Red.

Can I use Cardinal Purple instead of Bright Red?

Not as a straight swap; see the closer alternatives below. Loose match (ΔE 21). Cardinal Purple is noticeably darker, cooler than Bright Red.

Can I use Bright Red instead of Cardinal Purple?

The same difference applies the other way round: Bright Red is noticeably lighter, 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.