ΔE 15.4, loose: different enough that you should pick on purpose. Alizarin Crimson Hue is a little darker, more muted, cooler than Mephiston Red.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 15). Alizarin Crimson Hue is a little darker, more muted, cooler than Mephiston Red.
The same difference applies the other way round: Mephiston Red is a little lighter, 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 Mephiston Red on the colour wheel See Alizarin Crimson Hue on the colour wheel
All matches: Mephiston Red equivalents · Alizarin Crimson Hue equivalents